I don’t know how we got there, but use of “user testing” instead of “usability testing” is pretty widespread and I don’t understand it at all. We’re not testing users. We’re testing the usability of the design.
Language matters. We construct reality out of language. Language shapes how we see the world—it limits our perceptions, it tells us what kinds of things exist or don’t exist in the world. The power to name a thing lets us shape what that thing is for and who can use it.
So what we call usability testing matters. However, nothing convinces others like experts, so please do check out this blog post by Dana Chisnell from 2008: