"After the 1 year cliff, if you decide to leave you can exercise any options that you've vested up to that point"
If the options are not cash-convertable, is that because they haven't vested, or because they've vested and aren't preferred stock?
So whether you get preferred (which is usually issued shortly after the investment or founding) or common, you're unlikely to see that piece of the company be worth anything until the company sells, goes public or issues dividends. In the case of a preferred shareholder, you can also get some liquidity in the event of bankruptcy or shutting the company down.
To put it simply, when you are given options, you can exercise them by purchasing them at a very low valuation. Until those shares are worth something, you can not sell them.