Both the UK and US (and probably other countries) have museums in their capitals called the "National Gallery". Are they galleries or museums? Does the distinction even make sense?
For other cases it can depend on the purpose of the building and the collection. If it's about the art itself it's a gallery, if it's about the artistic movement and its historicity it's a museum.
I totally understand that this museum is interested only in works by a particular artist, and so fakes are unwanted even if they are good art. My point is you seemed to be making a distinction between the idea of a "gallery" and "museum", implying that galleries are interested as art-as-art and museums with art-as-historical artifact.
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.
