It depends what you mean by “suppressed”. The meaning varies between armies and periods. The modern NATO definition of neutralisation is very different to the WW2 one.
A pinned unit is normally one unable to advance by fire and movement, in which case the drill is to go on shooting at the enemy until the platoon Co tells you something different. A suppressed one is presumably in a worse state. Wait until whatever is causing the suppression goes away and resume your previous mission?
A snippet I have recently picked up from a summary of the work of 2ORS in North-West Europe says (quoting verbatim):
“Four degrees of severity of morale effect can be distinguished; they are:
(i) to stop movement,
(ii) to stop firing — neutralisation,
(iii) to produce some sort of longer term neutralisation which persists for a time when firing has ceased,
(iv) to produce a complete collapse.”
This seems to me a very neat classification, ripe for thieving by the sensible wargames rule writer. I don’t think it would be too far from widely-accepted terminology to call these “pinned”, “suppressed”, “neutralised”, and perhaps “beaten”. Although those aren’t all approved APP-6C effect verbs, the current distinction between suppression and neutralisation — that neutralisation lasts for some time after the fire is lifted — is preserved. For wargames purposes one might simply remove “beaten” elements, not bothering to differentiate between psychological collapse and physical destruction. I quite favour keeping them around, so that they can be taken prisoner — the lack of prisoner-taking in most modern tactical rules continues to be, as Wells put it in “Little Wars”, “a feature at once barbaric and unconvincing”. I suspect that “neutralised” troops would also usually give up if overrun by enemy infantry, or perhaps try to run for it if they approach too close. Exactly what combinations of terrain, visibility, enemy proximity, and weight of fire produce what reactions is something I have no good data on, but I imagine that people do not usually attempt to run from dug-in positions.
All the best,