I can almost remember the first time I had ever heard/saw the word 'equivocate', probably in some junior-high vocabulary lesson. Like with many latinate neologisms, at first blush it sounds weak and meaningless, its constituent parts don't combine directly to the given definition.
But my memory of the definition was that the teacher (or authority, or my memory of those) said it meant 'to lie, to present a falsehood'. The word sounds like a euphemism to me, an obscurantism, instead of baldly stating 'a lie'.
But now many years later and many uses and hearings of it, I find that the dictionary rendering is essentially 'to be ambiguous with the intention of misleading'. And that is definitely not 'lying'; it's close, and it's related, but it is not the same.
So now, I want to really know, which is it? Is it 'lying by willfully misleading with ambiguous language' or is it 'willfully misleading with ambiguous language, but can also be used for "lying"' or just 'willfully misleading, not lying per se, you'd have to do something extra to be considered lying'.