Keep in mind when you say "stock options," it can mean different things. The first thing that comes to my mind when you say "stock options" is options trading on publicly traded companies. That is buying and/or selling contracts of puts and/or calls.

The second is "stock options" at private companies as compensation, which is what you are referring to. There are many variations on how this works.

I've seen companies, as a bonus, grant what amounts to a call option that can't traded and only exercised at some point in the future. This may be free or you might have to pay for it.

I was once given stock as a bonus at a startup, making me an owner. Being an owner didn't pay me any sort of dividend, but it massively complicated my income taxes by giving me a K-1 in May (after April 15th). Additionally, I owed tax on my percentage of ownership, which was really a pain. The other gotcha but I wasn't allowed to be an owner unless I worked there. So when I quit, I got cashed out at "fair market value," which was a B.S. number they made up and gave me a couple thousand dollars. I also got diluted by half while I was an "owner." The experience made me very leery of ownership. Now I just look for salary.