A museum is ultimately a place where items of interest are kept. Most museums also have galleries, where items of interest are displayed. There are museums for almost every interest, from science to lingerie, and there are also galleries of every kind - but not every gallery is attached to a museum.
Items displayed in a gallery may belong to a private party, or a company, or an institution other than the gallery itself. The inventory of items kept in a gallery may be constantly changing. The gallery itself may never have a legal title of ownership for an item on display. The emphasis of a gallery is on presentation, and often on selling.
The emphasis of a museum may be almost anything, but usually one of the goals of a museum is to educate its constituency about the area of interest it represents - and a museum keeps items useful to this goal in its collection. The inventory of a museum collection may (but is less likely to) be constantly changing, but there is a focus and a central concept to guide what is taken in and what goes out. The museum may possess items on loan from individuals, companies, or other institutions - however, the museum is very likely to own, or have a legal role as perpetual guardian of, the majority of the items in its care. The museum may have no obligation to display its collection; it may only be available to researchers, for example.
It is the process of keeping these items of interest, and the additional process of educating a constituency, that is usually encompassed by the term museology.