I can't answer the question from a search committee point of view, but sometimes people get adjunct appointments so that they can officially co-supervise a graduate student, so there is no teaching involved. I know of one situation where that was the case, but I don't know how common that is.
This is how it works here, an R1. We have a list of maybe two dozen adjunct faculty members that have tenured, tt, or research (usually at federal labs) positions elsewhere. These are not paid positions and the faculty serve on graduate committees. There is no teaching involved. One does have to be approved for adjunct status and the term is for 5 years (renewal is possible). One of the adjunct faculty members retired to this community to be closer to his daughter. When the department and university realized that a
Big Shot biologist was in town, they offered adjunct status so he could have library access, a small office, email, etc. Basically a small place to hang his hat when he needed it.
The non-tenure track faculty members that teach are called visiting assistant professors, instructors, lecturers, or senior lecturers (there is a non-tenure track career ladder here).
Here, most adjunct title holders are those who have their entire appointment in another department, but basically have a title so that they can get grad students from those departments, or guest lecture, or whatever.
Ex: mechanical engineer with interests in applied physics is TT in Mech. E, but also has Adjunct <whatever title he has in ME>. Or chemical physicists sometimes get them.
Renewal is
definitely on the cards for such faculty members - and while there's a rule saying they need to be reviewed every so often, I've not heard of such status being yanked very often.