10% equity in a company can mean several things. What it means depends on the type of equity it is. In companies there are two classes of equity: common stock and preferred stock.
Common stock is equity that is allocated to employees. When this equity takes the form of incentive stock options (ISO) or non qualified stock options (NSOs) it has to be vested and purchased. When this equity takes the form of restricted stock awards or restricted stock units an employee has to vest it but not purchase it to own it.
Preferred stock is equity that is purchased by investors. Unlike Common Stock it does not need to be vested.
10% equity in a company may mean that it is held by an investor and therefore the investor owns 10% of the company or 10% equity in a company may mean an employee has the right to vest and/or purchase the equity in order to own it.