A spec, short for specification, comes from behavior driven testing, and encourages the mindset where you are defining ‘what’ the software does.
Calling it a test leads to a much more general way of thinking about the code, and does not reinforce the idea that you should be testing the interface (instead of the implementation) as well.
That said, regardless of how you write them, or what you call them, the point is to have an automated way of verifying the correctness of your code, so that you can proceed with confidence.