English is not my first language, so I always assumed blood and bleeding refer to any red liquid. I mean, we talk about blood oranges [0] and bleeding trees [1] and no one assumes there is any real blood involved.
I would guess that most people are, just as most people who refer to menstrual blood intend to imply that it is actually blood.
Is menstrual blood actually blood? That's not a question with a definitive answer; it is obviously different from the normal kind of blood you'd find in blood vessels, but it's also fundamentally similar. "Blood" is not an elemental or even homogeneous substance, so it can be hard to say that something isn't blood.
But most people who refer to something as "blood" have never given it a minute's thought. If you cut meat and get a thick red liquid, of course that's blood. Where else would blood come from?
Is it? Maybe I'm odd in this regard, but knowing that blood coagulates and having seen how blood sausages look like, I implicitly understand that "meat bleeding" is not actual blood.
[0] https://en.wikipedia.org/wiki/Blood_orange
[1] https://en.wikipedia.org/wiki/Corymbia_opaca