My theory is that it means not the actual Indies, but a place like the Indies, but to the west. I suspect Europeans at the time though of India less as where the Indians live and more like a place to get cool stuff, and cool stuff was indeed found in the West Indies too.

A bit like chicken of the sea. It’s not that they’re saying that tuna is a form of waterfowl, just that the two have common applications.

"The Indies" referred to the known archipelago in the Indian Ocean (now Indonesia and the Philippines). The Caribbean is also an archipelago, so if Columbus believed himself to be in the Indian Ocean, it's not that odd for him to assume he'd reached the western end of the same archipelago.

India is not a collection of islands, it's unlikely that Columbus mistook an archipelago for a known vast land mass.

If he thought it was India then it should have been the East India ...

Also, I think Indies was used to refer to Asia in general, rather than specifically India. But am open to correction.