Sorry that is not wainscoting BTW Post a picture of your space that is the only way to get help for your space.

Wainscoting is a broader term referring to decorative paneling used for centuries as: a) a wall accent; b) insulation and; c) to prevent (and cover up) damage to walls. It typically is made of wood, and covers the lower three or four feet of an interior wall.

I’m not sure what to call it to be honest

I was mostly just looking to see if it’s ok to use the same wall paint on the trim as well, or do I have to use a trim paint. I want a very cohesive look

Using the same color for the walls and trim can look really nice. I would use a different finish, such as satin or eggshell for the walls and semi-gloss for the trim and doors.

OK so whatever you call i... if you go two sheen's up it does add more depth. Just remember the flatter you go the harder it is to keep clean.

So you can do different wall sheen in different rooms and that also adds depth/contrast from room to room if you have an open plan house.

The shinier the sheen the darker the look.

P.S. I think it is called molding but I think we know what you are talking about. :)

Do you mean the higher than average baseboard at the bottom of the wall?

Would keep it all the same color as the wall.