The above is true (the "standard" I think), but the sequence can also change based on the professor's qualifications. I work at a university and deal with contracts and promotions on a regular basis, and we've had professors hired at the associate or full level, or transition from assistant to full with tenure, just based on how well-known they are (past research and such... not necessarily teaching status at other universities; we've had a few come in with zero prior teaching experience, but insanely impressive credentials in terms of publications and such).
In terms of timing, again it depends on the type of work you're doing... I've heard of some profs not getting tenure for 10+ years after their initial hire date, and others who are tenured within a year or two, mostly based on evaluations and research.
But yes, what paramour said is standard....
assistant --- associate (+ tenure) --- full
🙂