Normally, provided you have the correct engine code (family), there are relatively few differences in the guts of the engines.

Often, for example, the 0038 is the same as the 0001 aside for the 0001 being california spec with (maybe) a different carby with different jetting, catalytic muffler, etc

Try typing in 31S977-0009-G1 to the briggs https://www.briggsandstratton.com/na/en_us/support/manuals.html#

A IPL should come up

Then if you are curious, try 31S977-0005-G1

I would be surprised if the guts of the engine were severely different

Hope it helps

Regards