I see these three expressions used with the same meaning especially by people with programming background:
  • something count
  • number of something
  • something number

I am quite sure that the first two mean the same thing (how many are there of something), but I am not sure of the last one. E.g. in case of a book "page count" and "number of pages" means how many pages are in the book, but to me "page number" seems to refer to the ordinal number of a page.

What is the correct use and meaning of these three expressions?

Thanks for the answer in advance.