What are the different parts of a toilet seat called

You need to identify the toilet. There is often a brand logo under the toilet seat, between the bolt holes.
That said, it appears to be a Duravit “darling new” wall toilet. There are two or three models within the range, each gets its own seat/cover. Measure the length of the top of the bowl from wall to front edge and it will correspond with the spec online at www.duravit.us. It looks like the elongated version which probably uses toilet seat 0063390000, but you should check.
Good luck!

Yes, it's trivial. The seat is held on by bolts that go through the toilet and are secured underneath with large nuts. These days the nuts are usually plastic and designed to be tightened/loosened by hand.

The spacing between the nuts is standardized, at least in the US, so the only measurement you need is front-to-back. There are a few different sizes, but basically the break down to "circular" or "oval" and a generic seat of the right type will almost always work fine.

It will usually come with fresh mounting nuts. Insert the bolts through the holes, reach underneath and install the nuts firmly in place (you may want to try wiggling the seat a bit to make sure the nuts have properly centered themselves and seated", and you're done .