Exactly right on the repeater -- you communicate with the ISS on a VHF uplink and it rebroadcasts your communication on a UHF frequency (Earth stations typically run in a single band with a small offset). It's hard to talk to the ISS because it's moving so fast that there's a Doppler shift in the frequencies, but it's definitely possible with cheap gear (I've picked it up many times, but never tried talking through it). People aren't using it to communicate per se, more just to make brief long-distance (DX) contact with other amateur radio users.

There are also occasional opportunities to speak directly with people on the ISS (or more commonly, receive telemetry or slow-scan TV images).