All walkie-talkies are made to work on specific frequencies that the government (in the U.S., the Federal Communications Commission or FCC) reserves for different types of transmissions. Police and firefighters, for instance, have their own frequencies so that business and public signals don't interfere with emergency communications. So you can go ahead and put down that fire hose and the badge you made from tin foil -- the authorities don't want you messing about on their channels.
As you already know, FRS and GMRS frequencies are made for public transmissions. The FRS and GMRS channels overlap at some frequencies, but the actual radios that access these channels have some distinctive differences.
FRS handsets come with fixed antennas and are limited to 0.5 watts, making them very low-powered devices that often only work at a range of a few hundred feet, so it's unlikely that your radio will ever interfere with a neighbor's a few blocks away. Those kinds of walkie-talkies are just personal-use devices, and anyone can transmit on FRS bands for any reason.
GMRS devices can be much more powerful, at up to 5 watts, or about the same power consumption of a smartphone that's using all of its primary features. What's more, GMRS systems can be used with repeaters, which are devices that boost the range of the radio signal. In either case, GMRS devices always feature better range than FRS-only handsets.
Keep in mind that there are plenty of hybrid FRS/GMRS radios available. These walkie-talkies let you transmit on both groups of channels. However, when you're transmitting on FRS, the handset's power automatically drops to 0.5 watts.
There's another critical difference between GMRS and FRS. Although anyone can use the FRS channels, only licensed radio operators are allowed to use GMRS frequencies.
That's because these radios are more powerful and more likely to cause interference with each other.
Licensing is simply a way to reduce congestion on GMRS channels. However, many people use GMRS radios and disregard license requirements because the FCC generally doesn't enforce these regulations.
FRS and GMRS are North American communications standards. In Europe, walkie-talkies mostly use PMR446, or frequencies at around 440 MHz. You can't use a PM446 radio to work on FRS or GMRS, or vice versa. It would be illegal to even try. So when you're traveling abroad, it doesn't hurt to verify that your radios operate on a legal frequency. In extreme circumstances, transmitting illegally on the wrong channels can result in fines or even jail time.