Bifocals, also known as multifocal lenses, provide correction for both near and distance vision, as well as astigmatism if needed. These lenses help you see better both close-up and far away when your eyes can no longer change focus due to age/presbyopia.
Progressive lenses correct your vision for near, intermediate and distance, as well as astigmatism if needed. Please be aware that it takes about a week for you to adjust to them if you haven't worn them before.
Trifocal lenses provide correction for near, intermediate and distance vision, and for astigmatism if needed. They're most often used for jobs and tasks that require three focal distances, such as piloting an airplane.