The word wire usually describes a flexible strand of metal used to conduct electricity. However, there is a kind of non-flexible wire which can be used to transfer mechanical motion. I guess "rod" wouldn't accentuate how thin it is, especially if a device has a rod providing one type of motion, and a very thin, but very rigid "wire" providing a different one.
"Solid wire" just means that instead of many thin strands there is just one thicker piece of wire in the core.
The wire which I'm talking about doesn't have any insulator around, and it is rigid and elastic like a rod, just very, very thin.