I currently have a Delta single handle shower faucet in my shower. I want to change it out for a different single handle style, which is also a different brand. Are the valves behind the wall the same type of valves for all brands, or do they differ?

They usually are sweat soldered to 1/2 copper or solvent sealed if CPVC. Sometimes plumbers will use a transition fitting from copper to CPVC and there may be a fitting like a hose coupling. Depending on the house age, fairly new, you may have PEX. Rarely will different brands and sometimes different lines of the same manufacturer swap out. If you can get behind the valve, say in a closet wall, cut an access hole and take a look. Why not try to find a new plate and handle. HD and Lowe's carry some or check online. Good luck!

So I am such a DIY dummy, what would I be looking for? The shower is being remodeled, but the tile backboard is already up and cut in a circle around the valve. Would I just have to see if it is similar to one I buy? I have been looking for a new

Possibly. Take the old plate and handle to Home Depot or Lowe's and see if the holes line up. A single handle is usually held on with a set screw and the plate is usually held on with 2 screws. You might get lucky. Hope this helps.