FDMA IS Frequency Division Multiple Access.
Technically, if you wanted to, you could apply the term to any non-direct sequence spread spectrum non UWB (UWB - "Ultra Wide Band") radio boradcasts...even regular AM and FM broadcasts that are otherwise not further multiplexed in some way so as to contain more than one message path within one RF channel content. And, yes, I know stereo FM is multiplexed but trying to keep it simplified here.
USUALLY, however, FDMA is used in a "system" context. In the early days, wireline telephone ruled and when they started trying to find ways to send multiple voice streams down a trunk line one of the first technologies used was to upconvert the voice into a higher frequency band, RF, and then subdivide that into separate voice channels...all analog technology...hence "FDMA - Frequency Division Multiple Access".
Another usage was in satellite technology - again, mostly telephone driven. Here again, you would have one big "pipe" that was usually a large bandwidth that was then sub-divided into smaller channels with independent voice paths. Again, classic "FDMA".
When digital technology became cheap and widely available enough to be practical the concept of "TDMA - Time Division Multiple Access" became really practical. The concept could, in theory, be applied in a purely analog fashion but is/was problematic and not widely used. However, once the voice could be properly quantified in digital format it became relatively "simple" to apply the concept with fast processing to interleave two or more bit streams, each dedicated to a single voice or data path, using precise timing to keep each stream separated in time.
But digital signals can also just as well be handled by the old FDMA methods, of course. In fact, they usually are anyway even if they are further separated by time division methods as in the case of most LMR (Land Mobile Radio) applications.
Fast forward to today and the advanced digital trunking systems used and you once again, get the multiplexing concept re-applied.
In general, the FDMA vs. TDMA "battle", "debate", whatever, in terms of today's system architectures is how the SYSTEM handles the multiplexing - whether it be by time division or by frequency division, with the "systems" usually being trunked LMR or cellular telephone in nature. As stated earlier, even so-called TDMA systems are ALSO FDMA because each RF carrier is separated by channels BUT each carrier, in a TDMA system, then has separate "time slots" effectively becoming two (or more depending on the TDMA version used). In, however, a purely FDMA system, no further multiplexing is done outside of the finer subdivision by frequency.
TDMA, due to the usual requirement for a very precise and centralized time signal for each subscriber unit to synchronize with in order to allow them to separate the time slots effectively in both uplink and downlink paths to the repeater normally require the repeater to provide that synchronizing timing information. Newest technology by Motorola and others can allow simplex TDMA between mobile or portable units by essentially making one unit in a group the "master" and all the other units in that group time sync off that master and allow the usage of TDMA to provide more than one talk path per carrier even when no centralized repeater timing information is available. However, in most cases, TDMA is not used in simplex digital communications and the full RF bandwidth is usually used for one digital voice path whether it be a nominally TDMA or FDMA system so, effectively making the TDMA units FDMA only.
One big "neat special application" of the above, however, is the use of something called a "simplex repeater" which, in TDMA terms, can be effectively implemented by setting up a central unit in a high central location that can receive on one time slot and transmit on the other time slot. This effectively makes a "repeater" out of this station but, unlike a normal duplex RF repeater that requires the ability to transmit and receive simultaneously on two separate RF frequencies, this type of system does not require a duplexer and or separate antennas, etc. - it is all done using just one RF channel and the "repeating" is done on separate time slots. An additional advantage of this system is the ability of the subscribers to seamlessly move off the repeater into unit-to-unit simplex mode with the loss of the repeater signal without the subscribers even needing to switch to "talk-around" as in normal legacy analog or digital repeater scenarios (as I understand it - that is what I have read but have not dived deep into this so do your own research here to confirm).
Now, with regard to FDMA - that "old" multiplexing concept hasn't "stood still" with the rise of advanced digital radio systems. Now we start to get into the "battles" that spring up between different companies providing LMR products and how they embrace their "preferred" technology and produce competing products accordingly.
So we get, as a good example, Icom and Motorola. Icom (and initially, Kenwood) embraced an advanced digital FDMA systemology called "NXDN" that used very precisely controlled centralized RF carriers and extremely tight IF filtering and/or DSP (Digital Signal Processing) IF and post IF digital filtering and processing plus advanced vocoder technology to cram voice frequencies into a very narrow bit stream so as to provide extremely narrow digital RF voice paths seperated only by frequency but into, as stated, such small RF channels that could not practically be applied to analog FM channels (the deviation becoming so narrow, then, that any real advantages of the use of analog FM are pretty much negated) and THAT, grasshopper, is what most in the LMR world now mean when they bring up "FDMA" these days!
Sorry for the admittedly long run-on sentence...
Anyway, Motorola, meanwhile, embraced the tried-and-true TDMA concept and went with DMR which inherently uses a TDMA method.
When the (latest - there have been others in the past, oh yes!) FCC narrowband mandate came about, Motorola crammed the "bandwidth equivalent" concept down all throats stating that within a 25 kHz bandwidth (and later 12.5 kHz bandwidth) they could have two voice paths resulting in an "equivalent 12.5 kHz" (later "equivalent 6.25 kHz") bandwidth.
Only if you define the bandwidth solely in terms of modulated RF carriers can you call this to task. So, even though one DMR carrier may occupy the wider bandwidth it DID allow two voice paths within that wider bandwidth so was, effectively, "equivalent" to having two separate RF carriers in two narrow channels that together would equal the wider bandwidth of the DMR signal.
So, then, you have the "argument" between Motorola and Icom. Icom can claim that only they, using an advanced digital FDMA method, actually provide a true extremely narrow frequency separated methodology to provide separate voice paths per RF carrier. But Motorola, (and DMR in general) still can claim - in the final net view, "what's the real practical difference?!" DMR uses TDMA to cram two voice paths in the larger RF modulated carrier bandwidth so makes the capacity (relative to the stated RF channel used bandwidth) the "same". After this you get to the finer points of occupied bandwidth and adjacent channel power which I am not going to delve into here.
Kenwood initially went along with Icom in embracing NXDN only but later submitted to the inevitable popularity of DMR, helped significantly along by the backing of Motorola, and began producing DMR subscriber units. In fact, they now have units that can do multiple protocols, P25, DMR, and NXDN, simultaneously (well, actually, any two of those).
So back to P25. P25 has actually been around a long time now. "Phase 1" of P25 was all really just based on replacing analog FM with a digital modulation equivalent and not as any method to add capacity. It was, therefore, "FDMA" only but not really making the occupied bandwidth that much less than a typical analog FM system. I think they started with a 25 kHz bandwidth and then later went to 12.5 kHz along with the narrowband mandate; I think they can do 6.25 kHz but am not sure about that (read - do your own research here). Phase 1 could be applied to simplex, repeater conventional, as well as trunked systems. Anyway, "Phase 2", on the other hand, was defined from the start as a TDMA system and included trunking protocols that allowed two time slots per occupied RF bandwidth. In this sense, it is "like" DMR" but DMR is a newer and more advanced (in some ways) technology. But "Phase 2" P25 really is TDMA and can provide double the capacity of a FDMA only Phase 1 system. When conventional (non-trunked) or simplex, however, P25 is usually Phase 1 only but, I think, now some conventional (non-trunked) repeater systems are being used as P2 TDMA - again, do your own research on this as I am not sure about this.
Another advantage of TDMA RF systems vs. FDMA only (in its current advanced digital implementation) is "less plumbing" at the repeater end. This is because, with FDMA systems, you need speciallized tightly tuned duplexors, filters, etc., that help to make the tightly spaced ultra narrow signals practical, and you still need separate RF channels per voice path just as with old legacy FM and digital conventional repeater systems. TDMA, it can be argued, is "easier" to double the capacity of one repeater allowing two simultaneous (from a human user perspective) per one repeater in a conventional system WITHOUT making it necessary to add additional RF components. This makes it more "palatible" to many business users relying on more and more support from "IT" departments who are computer savvy but not usually "RF savvy". TDMA can be thought of in the sense that the "heavy lifting" is done more in the computer processing and programming arena and not as much in the RF arena as a fully NXDN type FDMA system. There is a LOT more to this than I am going to go into here and both system methodologies have their adherents and proponents, detractors, etc.
Sorry for the length and detail above but I hope it helps you grasp the "FDMA" vs "TDMA" "discussion" better in terms of today's modern LMR system implementation concepts.
-Mike