So I received my M&P FS .40 and I want to put a 9mm barrel on it.
I noticed Storm lake sells 2 barrels the 9mm Match barrel and the 9mm Conversion barrel. is there any physical difference apart from the conversion barrel being 20$ more expensive?

Storm Lake Barrels Barrel 9MM 4.25" Stainless Match S&W M&P SW-MP-9MM-425-OP-00T

As I understand it...

Yes, there is a difference.
The conversion barrel is a match grade 9mm barrel that you put into an M&P .40 to convert it to 9mm. The other barrel is a match grade barrel that goes into an M&P 9.

So, if you have the M&P 40 and want to shoot 9mm, you need to get the conversion barrel.

BTW I wish I would have seen your post sooner as you found a great price. I just purchased the conversion barrel for my M&P 40 and paid $133. Don't forget, you will also need 9mm mags. Cheapest I have seen is from 44mag.com.

Well the one i posted is a 9mm batch barrel not a conversion they sell the conversion one for 120$.