It's an assistantship. At least at my (public state) university, an assistantship means that your tuition is waived (fees are not) and you're paid for work based on a % of hours you are expected to work. There are administrative variants, teaching (where the pool of grad assistants come from), and research--the difference is where the budget comes out of and what kind of work you're doing.
Research assistants are funded by whoever's heading the research (so you're reviewing papers, doing applied work that's being paid for by someone else, etc). Administrative covers higher-level tasks that you don't want to pay a civil servant for, but don't want the people doing it to change every semester. Teaching assistantships are where you get the pool of grading-slaves.
In my department, TAs and administrative work comes from the department funding. My university has a glut of foreign students (my lab is comprised of mostly Indians) who can't actually work anywhere else but on campus, so every position (even non-related ones) gets applied for by them. Which then frustrates the heck out of the people offering the job because they have to at least sift through the 50+ non-qualified students to get anyone on the position.
IAAGS (I am a grad student)
