Unity is actually pretty inconsistent about their naming. In some parts of their docs they call it UnityScript:

http://docs.unity3d.com/Manual/CreatingAndUsingScripts.html

In other places they call it JavaScript:

http://docs.unity3d.com/ScriptReference/

And in the Unity Editor when you use the Add Component / New Script, they call it "Java Script"!

Everyone would be better served if Unity would call it UnityScript consistently, since as you mentioned, their language isn't JavaScript but is a fairly loose adaptation of it. It's more of a JavaScript-like language than real JavaScript.