And I'll put it another way. (your post was fine Harvey):
There are several different digital radio modes now. Digital Mobile Radio is one mode. Icom's Dstar is another. Yaesu's Fusion is another. There is also Tetra, P25, and the commercial Icom and Kenwood flavors, which I don't know a whole lot about.
The three most popular now in ham radio are Icom's Dstar, Yaesu's Fusion, and DMR. The first two are basically proprietary to the perspective manufacturer. If you want to go that route, you need to buy that brand of radio, or get something called a software dongle, which is basically a fat usb stick that plugs into your computer.
DMR is offered by several manufacturers. The highest cost radios are made by Motorola, all the way down to the lowest cost radios made by a company called Tytera. All DMR radios can talk to each other, for the most part. I say for the most part, because as you go economy, you can sometimes get some audio issues, firmware issues, etc. DMR repeaters are linked together through the internet. An individual can put up a DMR digital ham repeater, give it an IP address, and all the DMR repeaters linked together can be configured to communicate with each other.
DMR has what's called talkgroups. There are LOTS of DMR talkgroups. Repeater owners decide which ones they want on their machine. So for example there is a talkgroup 310. You program that talkgroup into your radio, and are able to talk to anyone on any repeater that also has this talkgroup in their radio, and in the repeater they are using somewhere in this big wide world. There are DMR repeaters everywhere in the world. There are many local, regional and worldwide talkgroups.
The same can also be said about Dstar and Fusion. There are Dstar repeaters linked over the net, there are Fusion repeaters linlked over the net. Yaesu's Fusion is the newest flavor of the three, and is picking up steam because Yaesu has been offering $500 repeaters for that mode. It's a great price for a repeater, and many people are putting them up.
There are no links between Dstar and Fusion, or Fusion and DMR, etc, that I know of anyway.