P trap YEAH, YES Approved, GREAT Choice.

S trap NO, BOO, Verboten, forgetaboutit, terrible BUT some officals have been known to accept less quality and take the money and run.

Baffle used on Bell traps (NOT for inside a structure) normally found on a catch basin for storm water but some call the bell a baffle.

Baffle used on grease interceptors / grease traps to slow the waste down allowing the grease to float on top and the cleaner waer to flow under the baffle

You may be thinking of a back water valve (check valve) used to prevent sewer water/ storm from entering a structure during the public sewer being over loaded

"In a situation where you can't use a P-trap or a S-trap, there is a "baffle" type of adaptor that can be used. Can you give me the specific name for this?"

Yes Illegal comes to mind

Are you thing about a Trap Guard?

http://www.trapguard.com/

It is approved, but not everywhere.

http://www.trapguard.com/approvals.htm