A C flute is another name for the western concert flute, silver flute, or flute. Those names all refer to the same instrument, and it's the one you see in the front row of a concert band or in the middle of an orchestra. The name comes from the fact that the flute is in the key of C, which is concert pitch. It doesn't matter if the flute has a C or B footjoint, though, the name and transposition will stay the same.