Shiplap.

We had a discussion of this over on the Houzz forums so I remember it. It depends on what your boards are. If you do tongue-in-groove you don't need to install it over wallboard, because there will be no gaps for insulation to poke through or whatever. If you are doing boards and just butting them up against each other, you may want to do it over wallboard so you don't see into the wall cavity.

Here's the discussion. Some good info in there if you poke around.

[https://www.houzz.com/discussions/need-advice-on-interior-lap-siding-dsvw-vd~1116913[(https://www.houzz.com/discussions/need-advice-on-interior-lap-siding-dsvw-vd~1116913)

thanks

over sheetrock. it isn't just about insulation showing...it
is about the air tightness of the wall.
even t&g has air leakage.
air moving through insulation de-rates its performance.

invest in the sheetrock under the boards.
it is a worthwhile cost that will be long term.

best of luck.

In our area, yes, shiplap had to go over drywall (including first floor ceiling) due to fire safety requirements -- though the drywall might not have been required on the interior walls.

There are no fire rated partitions in a single-family home. Even the garage separation is essentially an unrated smoke partition. But even unrated drywall will delay the spread of fire from room to room.