Is it correct to refer to stock options as “equity”?

Putting aside whether or not options are objectively definable as equity (I think that's a really tough nuanced question with no real objective answer) I think the biggest barrier between considering something to be equity or not ought to be what the vesting schedule is.

If there's a chance you can be screwed out of your "equity" (whether you consider that to be stock or options) by being let go or through some other trickery just before you reap the benefit, maybe that's the biggest characteristic of whether or not something is actually "equity".

I can offer you the equity of a billion dollars for being my employee in 10 years, but it doesn't matter if I'm planning on firing you in 7 years.

In casual conversation, or in a specific legal/regulatory context, or what?

Are the "stock options" something that one of the founders said over beers that they'd give to everyone next year, or signed-and-notarized-and-your-lawyer-says-it's-ironclad paperwork in your hands, or somewhere in between?

(What? No, I've never been burned on this. /s)

It’s a derivative of an equity, which I believe most consider an equity as well.