No, you can use the 316 filler metal with the same WPS. No change in F-No and all classifications are permitted, see Table QW-422.

Thanks.

Yes, unless impact testing is required.

What will happen metallurgically if 316 is welded with 308 wire ?
Agree with metengr re: both same F No. and also weldstan re: impact testing but one of the main reasons we have WPS's is to provide guidance to the welders / welding operators.

If 316 is fine being welded mistakenly with 308 then I see no problem with using the same WPS.
If however there is an issue with 316 being welded mistakenly with 308 then I think the WPS should be revised.

QG 101 requires specific essential and non-essential variables (QW 404.33) to be recorded.
Defining specific is the question.
Regards,
Shane

Many Manufacturers/Contractors make a list of filler metals/base metals combinations on their stainless steel WPS's. Because we had so many construction projects with newly hired welders, we made each WPS with base metal and filler metal to be used in keeping with DekDee comments despite the fact that a greater number of WPS's were required to be implemented.

Just to follow on from mine and weldstans comments.
Many welders do not have a clue what the specific base material is - 316,304,321 etc - to them it is just stainless steel and it is welded with the same technique and generally the same parameters.
Filler metal is generally the only difference and if you give a welder a WPS with 308 filler metal there is a strong possibility that is what he will use.