Yes, a shareholder is someone who owns part of the company, which is what stocks/shares are.

There are different stock types, though. Common stock is what everyone thinks of when they hear stocks/shared. You own a portion of the company and can vote on stuff, and maybe get some dividends.

Then there are preferred stocks which are basically a hybrid stock/bond with a fixed regular dividend. They also get first claim to the company assets if it goes under, but they usually don't have voting rights. Then there are subtypes of preferred stocks.