often, you can buy the works placed in a gallery, while museums you cannot. also, usyally, galleries have rotating stock depending on events etc, whereas museums have storage they rotate out of. additionally, galleries are not, most of the time, focused on non-contemporary artists and works, while museums have a substantial historical focus.

there is a distinction, thats why there are different words. outliers and exceptions not withstanding, since words and their meanings do not force their usage.