I've been offered a job recently as a lead developer at a small startup. They have no technical talent, and I'd be joining to build the product, do sysadmin work, recruit talented developers, etc.

The company already has some value, as they've already purchased a company and are basically throwing out the old team and building this new product.

The CEO wants a dedicated employee who will devote the next few years to this product, and I've been told I'd be considered "part of the founding team". So they offered me a 4% equity and a salary that's about half of what I'd make as a sr. engineer elsewhere. This seems like a generous offer for an early employee, though I'm clearly not being thought of as a co-founder.

As I was negotiating/being sold on this company, I was under the impression that equity meant stock given to me by the company over a period of four years (with the typical one year "cliff"). I found out that it's actually stock options that they're offering. So I'll have to pay for them (likely at a high valuation due to the initial investment). I'd be taking quite a salary hit, so I was thinking that the equity would make up for this. But I don't even know if I'll be able to afford to purchase the stock available through stock options.

Is it normal for "equity" to be considered stock options, and not actual stock? Does this situation seem fair to both parties?