Why do we refer to car manufacturer as 'Make'?

When I first encountered it years ago, I was pretty sure it must be a mistake. Although I got used to it, it still does not feel right.

What is the reason for that? Is it something specific to the automobile industry? Are there (maybe) historical reasons for it?

Make as in car make is not a recent innovation derived from the verb, as one is tempted to believe, but is based on the definition "the manner in which a thing is made". The OED's earliest attestation for this use of make is dated 1375.

No, the term make as a noun is not unique to automotive industry. In fact, the definition says:

the manufacturer or trade name of a product.

Even though it is often heard when speaking about cars, the word make can refer to any type of product. Consider:

There are many different makes and models of reel, which can be used for this type of zander fishing.

To be a pilot you need to know aerodynamics and a bit about the engines but you don't need to know the make of the fuel pump.