A banana clip is a fashion accessory typically worn by females that consists of two semi-lunar combs, joined at the ends, with the teeth interdigitating. Hair is held in place by the teeth.
The gun version of the definition that you refer to is actually curved magazine, one that is 'banana'-shaped. The use of the term "clip" to refer to long magazines that curve is a misnomer. People often call the magazines for 1911s "clips" and they are magazines, not clips. It is the magazine that holds the rounds so that they can be fired from the gun. Clips hold the rounds to load into magazines, but only on certain types of guns.
Guns like the M1 Carbine had magazines, but the magazines were loaded from rounds on a stripper clip. The clip with rounds were placed in the mag and the stripper removed.