A reasonable number of schools hire non-tenure-line, full-time instructional staff on a year-to-year or two-year contract. They may be called “adjunct” but there was a hiring process (rather than pulling one from the pool).
To confuse things further, your rank and your title may not be the same, and you may carry rank with you from a previous institution.
I am an “adjunct assistant professor” by title, though my rank is “instructor.” By university decree I may drop the “adjunct” designation on business cards and in describing myself (e.g., at a presentation). I am a non-tenure-line hire (that is, there is no research/productivity demand on me and I teach a lot of classes.)
I am on an annual contract that totals full time (more on this in the next paragraph). I started as a “visiting assistant profesor” but moved over to “adjunct assistant professor” after a hiring process. Either way, I’m in my 7th year of working here full time.
Since my contract (the amount of my time that I spend at the job for which I was hired) is at the .5 level, and I fill in the other .5 with work contracted by other programs (but for which there was not a search to fill me position), I am actually in two different statuses, both referred to as “adjunct” but one eligible for cost of living increases in the last round of raises, the other not. Since I receive one paycheck that does not separate my adjunct pay from my adjunct pay, oh, the fun we have making sure I have been paid correctly.
It recently became clear that this university system has no mechanism for promoting full-time, long-term, non-tenure-line faculty; even though we had been told that if we meet requirements for “tenure and promotion” (even though tenure cannot be extended to us), we could advance to “associate” or “full” professor. However, a recent test case revealed that this assertion is inaccurate because there is no specified evaluation process for this change of rank. If you’re in the middle of this, it’s fascinating and very emotional; if your not, it looks like people who are too obsessed with a role-playing game.
Meanwhile, at the community college I’m an “adjunct instructor.”
A few people call me “professor” (at the university), but most call me by my first name. I tell them that they can call me “First name” or “Dr. Surname,” but I’m not Mrs., Miss, Ms. or “Dr. [initial].”