What is a G-Check and what are the differences relative to other checks?
It's tough to tell based on your question, but I think you are talking about an inspection due to an over-G reported on a flight either by the pilot or the flight control system post-flight report.

Maintainers will do inspections of known stress points on the aircraft to look for breaks, cracking or loosened parts and then declare it safe for flight or fix anything out of tolerance.  For a low level over-G, this could be pulling a few panels.  For higher level over-Gs it could be 8 hours worth of work