OK, I can see how your definitions of those two things are tautologically identical. But this still goes with my point that both terms have many different definitions, so you can end up with situations like yours where the terms are equivalent.
Personally, I've never heard that definition of free will, to know that you are choosing; and for occasions where I don't even realise I'm making a choice (e.g. when failing to notice I've been given a false dichotomy, or which fork of a road I take on long walks), I still have what I would call a conscious experience of them… but then, for me, "consciousness" is usually "qualia" (but if the sentence is more complex then it may also be for example one of "not asleep/comatose" or "not subconscious/pre-conscious").
Likewise, my default (in the absence of further context, e.g. being on this website) assumption when I hear "free will" is that the person using those words means something like a supernatural soul, but the underlying physical phenomena which is actually backing this is some combination of hidden information and being too complex to predict, which is why we also witness animism in various forms
I dont see how I could exist, knowing that I can do things, without doing things.
Hence they are inextricably tied, to me.