What is an appropriate term for a (graduate) student who is meeting with a small group students on a regular basis and discusses with them the lecture and exercises? Or: Can someone explain me (as a non-native speacker) the difference between TA (teaching assistent), tutor and exercise group leader?
Maybe this should be a question on Academia.SE?
But I fear that the answer is "it depends on the institution".
At my undergraduate institution, "tutor" is a term reserved for undergraduate students engaged by the college to help out one of their fellow students who is having academic difficulties. Graduate student assistants whose job is to grade homeworks and hold office hours are called "teaching assistants". Graduate student assistants who additional also run exercise sessions are called "preceptors".
(In the education system associated to the health profession, "preceptor" are often synonymous with "clinical instructor". At Harvard, the word "preceptor" is used, among other things, to designate a faculty member teaching expository writing. Wikipedia also alleges that at some schools, certain mathematics courses are taught by faculty members termed preceptors; however I don't have personal experience to back that up.)
At one of my previous jobs, assistants (graduate student, postdocs, or tenured faculty alike) whose job is to run small-group (1 - 3 student) exercise sessions are called "supervisors". The same job at Oxford is called a "tutor".