Yes. The two main types are nonqualified stock options (NQSOs) and incentive stock options (ISOs). The names indicate their tax status under the US Internal Revenue Code. ISOs receive special tax treatment when all the rules and holding periods are met. For details on NQSOs and ISOs, including their tax treatment, see the relevant content areas on this website.
Most omnibus stock plans permit companies to grant both NQSOs and ISOs. However, companies tend to grant one or the other, or NQSOs to everyone plus ISOs for executives. Some companies are also granting restricted stock or restricted stock units (RSUs) in combination with or instead of stock options, or stock appreciation rights instead of stock options. Check your stock option grant agreement for specifics on the options you have received.