Hello Alostor,
So you're asking a girl out for coffee. In most cases, the girl will see this as a sort of casual date. I say in "most cases" because some of us can be a little aloof when it comes to the intentions of a man. If she is the kind of person who is analytical and observes then she probably picked up on the signals and put the two and two together. Most likely, she knows that this is a date. If she doesn't, then it's up to you to make that clear to her. Keep pursuing her, tell her, "This was nice. I really had a great time, and I'd like to do this again soon." And most of all, don't take too long to follow through after you say that otherwise she may think that this was just a friendly hangout and nothing more.
I hope this helps and good luck to you, Alostor!
Yours truly,
- M{r}s. Right
www.missus-right.com