Why everyone says "Rift" instead of "Archives"?

Cause its easier to type "Rift." That and you know what they are talking about either way so doesn't much matter to me.

Probably because people care more about the rift progression then archives in general.

Most people don't know the difference. People know what the Rift is, but they think the Tome is part of the Rift, or that Archives just means the Tome. A lot of people don't seem to know what the word "tome" even means.

I agree that people should put more effort into understanding the terms they're using before they use them, though, because as long as there's this widespread misuse of words, it just leads to a whole lot of upset and confusion. If there were more general clarity among the community about what The Rift actually is, for example, there would be a lot less confused people worrying about whether the Tome challenges are about to close right now.

Info in here about what?

You mean on the forums? That's true, but as much as I enjoy helping people out with their questions, I feel like it would be ideal if people didn't have to go looking on places like the forums to find out basic things like what "The Archives" means. It explains it quite clearly ingame - the only reason there's any confusion is because no one in the community bothers to use the right words for things and so there's a lot of what appears to be conflicting information floating around.