别 (bié) on its own can mean 'to fasten with a pin', 'to insert', so 别子 is literally 'fastener-thing' — anything that pins or clasps: a hairpin, a belt buckle, a brooch, a luggage hasp. Context tells you which.
memory
Same 别 as in 别针 (biézhēn, 'safety pin'). When you see -子 (-zi, neutral tone) tacked on, it's a noun-forming suffix, not the meaningful 'son'.
