Thin?  3 pins?  Yeah Appletalk.  If it has 4 pins and looks like S-Video, that's be ADB.  If it has 8 pins, it's probably serial.  Thick cable could be monitor, power, or other uses like special cable used for DOS compatibility card or Apple IIe card for LCs.

Always nice to see the cable rescued. Otherwise it may have gotten thrown out as unknown or "weird propriety" cable.