What is the difference between a HAM radio and a GMRS radio?
@AK9R summed it up pretty well.
I'll add that, for the most part, ham radio isn't channelized like FRS, GMRS or CB. These services are required to operate on specific frequencies or channels. These frequencies are hard coded into the radio and users aren't supposed to change them.
Hams can
technically operate on any frequency between the lower and upper limits of a particular band. In reality, especially in the higher (VHF and above) bands, there are various agreements specifying the spacing between frequencies and the offset for repeater frequencies. Most ham radios have memory channels, but it's up the user to program as they see fit. Most radios designed for the ham market allow the user to easily change operating frequencies, power output or emission type directly from the control panel (or programming software).
FRS, GMRS and CB are also limited (by rule) to specific emission types. FRS/GMRS are FM (with FRS being narrow band FM), CB can be AM,, narrow band FM or single sideband (SSB). Amateur radio has emission (or more accurately bandwidth) limits on some bands, but overall there are many more emission modes available, including various digital modes.
A few commercial radios have the necessary FCC type acceptance to operate on GMRS frequencies (462 and 467 MHz), UHF Part 90 commercial frequencies and the 70 cm (UHF) ham band (which doesn't require type acceptance). So in a
very limited context, a single radio could be used in multiple services providing the operator held the appropriate licenses.