I am now going to have to look up is this is a regional/dialect affair. Cord, wire, cable, lead.... before this I had never heard of any dislike here and considered them all perfect synonyms in both power and signals give or take cable occasionally also being a mechanical thing, though even there wire has some mechanical applications (a light, inextensible wire attaches at......). Actually come to think of it I can have a light cord in my bathroom/toilet and a dog/horse lead.
I might have considered it if you had said plug when people mean cord, which leads to the actual one of plug when people mean socket and vice versa.