The valves is the thing that actually mixes and controls the flow of the water. The trim is just the handle and face plate. That handle, though, needs to interface with that valve. The valves are all different between manufacturers, so trim for American Std might not fit a Delta valve.
Even within the manufacturer, not all trims/valves are interchangeable. One main dif is valves that allow pressure and temp to be independently controlled. Older valves might not support trim that has separate temp and pressure dials.
If you got the same trim from HD that's on there now, you SHOULD be ok.
The faceplate unscrews. It might be siliconed to yr tub surround, so you MIGHT have to delicately cut that bead of caulk.
The teflon tape is for sealing the threads btn the shower head and the shower arm. When u replace the head, replace the existing tape with fresh,new stuff.