This answer is related to fedja's. Many universities, at least in the U.S., hire various kinds of adjunct faculty to help with the departmental teaching load. (These positions are often called "visiting professorships", but I don't have in mind the kind of short-term research visiting collaboration that fedja discusses, but rather semester or year long positions, funded by the dept., not an individual, for the primary purpose of helping with the teaching needs of the dept. At least at my university, these are not offered by individuals; very likely the details of how they are offered differs from one dept. to another.) At my university, and I would imagine at others, the basis for the offering of these positions is quality of teaching.

Obtaining such a position, and doing well at it (so that one gets subsequent strong teaching recommendations) can be a foot in the door to a teaching-based academic position.

Also, at my university (and I know we are not unique in this, although perhaps uncommon) there are no math classes taught in lectures of 200; everything is taught in classes of around 30 or fewer students. So what matters is the quality of the teaching recommendation in relation to teaching such classes. Speaking more generally (and so less authoritatively), I would imagine that for teaching recommendations in general, the quality and strength of the recommendation is important (the applicant should have a record of good lecturing skills, sincere relationships with students, etc.) rather than the precise nature of the previous teaching experience. (After all, some new Ph.D.s will be hired to positions in which they might have to give 200 person lectures, but even if they have had prior teaching experience as a grad student, it is less likely that they will have given lectures to a class of 200.)