It's kinda both. The expression describes the sensation of almost remembering something. If you take a computer as an analogy, it's like you've managed to find the file the word is in, and you've double-clicked to open the file, and now you're waiting for the computer to access that part of the hard drive and open the file. You know how sometimes when you try to open a file and the computer kinda freezes for a little bit? "on the tip of my tongue" describes that sensation of the information almost being accessed. With a computer, this could just be a temporary thing, such as your computer needing to spin up the hard drive, or there could be something wrong with the file, and it never opens. Similarly, something "on the tip of my tongue" could mean I need a few extra seconds for my brain's "hard drive" to "spin up" (metaphorically speaking, of course), but it could also be followed with completely failing to remember what I was looking for.
The phrase refers to a moment in which you can't remember. If that moment is followed by you remembering the next moment, then the overall effect is that it takes you longer to remember. If it's not followed by you remembering, then the overall effect is of you not remembering.