DMR rules are the rules that vary the most across different sites. The basic premise is that they have higher power, but must be locked to semi-auto, have an MED and you will not be allowed to spam the trigger; usually the rule is "one in the air", so you have to watch your shot to completion before pulling the trigger again. However, there are things that can vary:
Power - I've seen lots of different power limits. 1.48J, 1.64J, 1.88J, 2.32J are all powers that I have seen for DMRs at different sites
RIF type - Some events and sites require the RIF to be a DMR in the real world. This usually means it has to be some sort of .308 calibre replica like an m14 or SR-25, or something like a mk12, VSS or SVD if it's not a .308 replica
Stock - Some sites mandate that a DMR must have a stock. Some don't. I don't mean like a fixed stock vs retractable stock, I mean in terms of not allowing something like a revolver or mk23 without a carbine kit to be used as a DMR
And yes, as has been said, people tend to look down on it when people put a scope on something like an m4 or arp-9 or something like that, up the power to DMR limits and then spam the trigger. It's mostly spamming the trigger though, that's the big no-no when it comes to DMRs. Cue the "that's not full auto, this is" video clip.