The majority of radio triggers are not compatible with each other, even if operating on the same frequency and from the same brand. There may be some semi-capability, such as Yongnuo's YN-560-TX transmitter being able to set off Yongnuo's RF-602 triggers, and the inter-operability of the RF-603, RF-603II and RF-605 triggers, but generally, do your research on the specific trigger you're interested in. The best site I've seen for doing research on triggers, lights, and compatibility is the Flash Havoc blog.
The "channel/group" protocol can be either on the trigger side (as with the above-mentioned triggers) or the camera/flash side (as with Canon's groups, channels, and ID codes in their infrared wireless and RF protocols). So, again, these can change depending on the triggers or brand of camera gear you're using. Don't assume compatibility of groups and channels unless both the trigger/receiver model match and the hotshoe protocol of the camera/flash match.
However, there are a few notable trigger choices that can get past the same-model restriction.
Canon's RF radio protocol is being cloned/supported by Yongnuo, Phottix, and Jinbei. That does not, however, mean all those systems support each other. :) Yongnuo has clones of both the 600EX-RT and ST-E3-RT Canon units that are supposed to play well within the system, if not with all the same capabilities. Jinbei's and TR-Q triggers seem to be dual-mode, supporting RT in one mode, but Jinbei's own cross-brand RF system (which includes small and large strobes as well as speedlights) in the other; they also make a 600EX-RT clone. The Phottix's Laso triggers also work with RT gear, as well as their own RT-compatible Indra studio strobe.
PocketWizard, RadioPopper, and Phottix all make triggers that interoperate with each other within the brand. You can mix both TTL and manual-only triggers, and they will all sync together, sometimes with group control.
And there is a class of triggering systems that are manual-only but manage to afford some type of remote power control either through a built-in receiver in a same-brand light, or through a quench pin hack for TTL speedlights. Yongnuo has the YN-560-TX and YN-560III/IV/-660/-720/560Li speedlights for this, with group on/off control with the RF-605. Cactus V6 triggers can control Canon, Nikon, Pentax, and selected four-thirds TTL flashes, and the Cactus RF60 speedlight. Similiarly, the RadioPopper JrX units can use an RPCube for flashes with quench-pin signals. Godox makes several non-TTL lights (speedlights and studio strobes) that also allow for remote power control (and possibly HSS) from an X1T or XPro transmitter.