I have a reason for asking this, but it’s really stupid, so never mind.
At my college we called them “section”, which I suppose was short for “discussion section”.
recitation period I think.
Never had one in college, but I led discussion sections as a grad student TA.
what the university called them is discussion session.
TAs and students might have other terms.
We called them seminar sections, because they would divide a big lecture section into four or five smaller seminars with different TAs.
We just called them “recitations,” not recitation periods.
At universities here smaller sessions outside lectures are known as tutorials, or more colloquially, “tutes”. The person running them is the tutor.
At MIT, recitation sessions - though many of them were taught by a real professor, often more senior than the guy doing the lectures. TA sessions were quiz sections.
At my university we call them tutorials. I actually hate the term because it sounds sort of remedial to me, and as a tutorial leader I don’t like being called a ‘tutor’, but what can you do?
Well, the main teaching language here was not English, so maybe I shouldn’t add that these TA sessions could have names like ‘assistentials’, ‘assars’ or ‘tutorials’. There’s one English-language programme where students seem to call those sessions ‘recaps’ (as in recapitulations).
Discussion sections here, section for short.
For some of my math classes, I had tutorials where the T.A. would answer questions that students had about homework assignments, class material, etc. It wasn’t an extra lecture, though.
For one of my history classes, I had a discussion period (or section? I don’t remember) where the T.A. would lead us in a discussion of the assigned reading for the class. Still not an extra lecture, though.
EDIT: Oh wait – is “extra-lecture” supposed to mean “outside of lecture hours”?
Yes. 
We called them sections. I didn’t know that that was short for discussion section until now and I was a grad student TA.
Discussion sections, or sections.
Section.
Tutorials. (Canada)
Generally, they were called recitations. In math classes, the same thing was called “math lab,” IIRC. Usually the recitation was led by a TA. A couple times the recitation was led by a second professor. In my computer science class, the lecture and the recitation were handled by two different TAs. I never had contact with a CS professor.
I think I had “quiz sections” as an undergrad. Although they were generally lead by the professor ( small, strictly undergraduate institution, few TAs), and generally did not have quizzes. Well, I guess they sort of had quizzes–they had homework problems to do in class, and then more to work on your own or in groups later . . .
Recitation