Interestingly, 'member' can mean either 'a person who belongs to a group' or 'a penis', as well as it is in Polish (członek) and East Slavic languages (член).
It somehow can also mean "a limb", although that meaning is rather dated and I'd only expect it in plural ("członki", which is different from the plural for "member of a group", which would be "członkowie").
Although a "member" could be a "part", a "part" is not always a "member". A replacement headlamp for a car, for example, is a "part", but is never a "member".