We have 2 college students in our group of 4. What exactly are RUSH Tickets and should we try these instead of the TKTS booth?

Studnet RUSH tickets, when available are cheaper ($20 range)than TKTS tickets BUT:
Usually for off-broadway, music, dance performance, not Broadway.
You have to get them at the box office a short time before the performance (hour or so before only?)with valid student ID
It's a way for theaters to get rid of really last minute tickets. You can't
[legitimately] get tickets for the others in a group this way. If the students want to try for a last minute deal, it's worth it for them to try

Following Broadway shows offer student rush tickets:
Blast - at box office after 6pm
Riverdance - at box office, 10Am for performances Tues to Thurs - $30
Full Monty at box office Tues to Friday - $29
Rccky Horror Show - at box office - $20
If You Ever Leave Me I am Going With You - at box office $15
Must have a college ID

We bought RUSH tickets once to Civil War. They got us in the theatre - but they were extremely blocked view. [I mean extreme. only 5-10% of stage view] Most Rush seats are.

We didn't need to show ID. And we don't look college like (anymore)

We also were able to change seate (stand or sit) once the show got underway.

GOL's made a very good point about the "rush" seats, "student" seats, etc. Quite often they are not good seats, which is why the theater is selling them so cheaply in the first place!
That scenario is far more often the case than the one cited previous by Nyer.
The obvious question to ask before bying the tickets is: "Where are they?"