Do dropcatch websites just register domains?

You are correct, when a domain is 'dropped' it is the end of the domain's lifecycle, and it is released by the central registry for public registration.

If you're using a dropcatch service and they successfully catch your requested domain it would be the same as a new registration in the domain's lifecycle, with the creation date being the same date as the domain was caught.

We have some more information on the domain lifecycle here if you were interested:

https://www.dynadot.com/community/article/qa.html?aid=5

Wow a lot goes into this