Cursor is Latin for 'runner'. A cursor is a name given to the transparent slide engraved with a hairline used to mark a point on a slide rule. The term was then transferred to computers through analogy
Yes , the link I provided also explains the etymology of "mouse". In short, the invention of a free moving cursor was initially called a "bug", but since the caret cursor was also called a "cat" they called it mouse. The first mouse pointers were operated by trackballs, so the physical device didn't resemble a mouse until later.
The subject in question is a "caret". It's also known by the more generic word cursor (or slightly more specific "text cursor") but seeing as there's a specific word for the item in question it makes sense to use that, even if both are appropriate. They're all a kind of symbol so we could just call it that. But that's even less helpful, isn't it.