A repeater transmits and receives at the same time. That is what makes a repeater full duplex.
So by your definition full duplex is simply the ability to receive and transmit simultaneously with no other requirement.
No repeater will allow everyone to talk and listen at the same time. You can not stand in the middle of a room full of people and understand all of the conversations going on around you at once but you can pick out one conversation and follow it.
The breakdown of the system you are describing is in you, not the system carrying the data to you. While an individual human may not be able to understand everyone at the same time it would be technically possible to understand everyone at the same time.
The point here is that it is possible, even if you cannot do it yourself. More importantly to the discussion of full duplex is the fact you can pick any one conversation and talk with the other person, and while they are talking you can also talk, with no destruction or loss of data. They can hear and understand you despite the fact they are talking themselves.
But a repeater is a device in a system, not the system itself. The system is NOT full duplex, it's half duplex. Only the repeater is full duplex.
I would argue the other side of that. A traditional FM repeater by itself is NOT full duplex, although when combined with correctly configured other hardware it might be a node in a full duplex system.
Lets define a traditional FM repeater.
A traditional FM repeater monitors one frequency (F1). When a signal meeting either the power level threshold requirement or a control tone requirement is present on F1 that signal is received or the squelch is opened and the audio is demodulated to base band. The base band audio is then applied to a transmitter that is keyed on by the same detection criteria as originally opened the receiver squelch (say a COR held active by the received tone or received signal level). The transmitter then transmits the base band audio on a separate frequency (F2).
In normal use stations A and B, using the FM repeater, will have a half duplex radio that transmits in FM on F1 and receives on F2. Station A keys up his radio and talks. If, before station A finishes talking and unkeys, station B keys up and tries to talk to A, two things happen. One, station B can no longer hear station A. And station A cannot hear station B. A third station, monitoring F2, will typically only hear one station, the stronger station that captures the FM receiver, or may hear an unusable mash/mix of the two stations.
So lets look at the definition of full duplex.
"Reference Data for Radio Engineers", 6th edition, defines full duplex as “Full Duplex: A type of operation that permits simultaneous communication in both directions between the called and the calling parties.”
"Buchsbaum's Complete Handbook of Practical Electronic Reference Data", Second Edition, defines full duplex as "Devices which transmit in one direction at a time are said to be operating in half-duplex mode. Devices which operate in both directions simultaneously are said to be operating in a full-duplex mode." and "In a full duplex circuit, simultaneous communications in both directions is possible."
"IEEE Standard Dictionary of Electrical and Electronics Terms", Third Edition. Defines full duplex as "Full Duplex (telecommunications). Method of operation where each end can simultaneously transmit and receive. Note: Refers to a communications system or equipment capable of transmission simultaneously in two directions."
Many online references put it the same way, but a quick look at Wikipedia (shudder) says “In a full-duplex system both parties can communicate to the other simultaneously.”
The important take away here is that all of these say essentially the same thing, simultaneous (more than one station at a time) and both directions (to and from each station). I would say a traditional FM repeater as they are typically configured does NOT meet this requirement. An all mode translator, on the other hand, might very well do so if combined with the correct end equipment at each station location.
T!