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.
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)
Practically - unless you're a real C-suite insider, "options" have a lot more ways to be worthless than actual stock shares. I'd innocently ask for details - then either run those past a lawyer before agreeing to anything, or just assume that the options were worthless.