They probably have different technical definitions in different specialized fields. I've been tinkering with electronics and chatting with electrical engineers for decades. To me, a "lead" means a wire that carries signal, not power, and often carries it to a measuring instrument. An oscilloscope has lead; a EKG has leads. A "wire" means something with a single electrical conductor that is reasonably flexible, and has a simple cross-section. A "cable" means something thick, with more than one conductor, and a complicated cross-section; a coaxial cable in which the ground conductor surrounds the signal wire; a flat ribbon cable that connects components inside a computer; an undersea fiber optic cable with hundreds of fibers.

Assuming that this is in the context of electrical wiring, no they are not synonymous. Leads in a wire are the ends of the electrical wire that have been stripped of insulation (jacketing). Cable is thicker than wire, have a central core, and may or may not have other wires that surround that core. Wire is a more generic term for conductors of electricity to/from a power source.