What types of equity are there?

This is a very complicated question actually. Equity is basically stock/ membership ownership/ percentage ownership. The name changes based on the structure of the company (LLC vs Corporation, etc). And the company can have (according to its bylaws or operating agreement) different levels of equity ownership shares available. For instance, usually the equity (I will call "stock" from hereon out) is either voting or non-voting stock. Voting stock is much more valuable than non-voting for obvious reasons. So, I would imagine that founder will have voting stock, whereas, new employees may not, depending on how valuable the employee is. If the employee is coming on as a CEO, CFO, CIO, etc, I would imagine that this employee would want voting stock, because a CEO, CFO, etc is super intimate with the company, and will play an integral role in the company. The value of the different stock is usually identified by calling it "class A stock" or "Class B stock". Be careful the names carry weight, not just legally but financially. Talk to a business lawyer prior to signing anything with a stock option.