There are seven that are commonly referred to. There are the two mRNA—Pfizer and Moderna. You have the two viral vector—AstraZeneca and Johnson & Johnson. Then you have the three subunit protein—Novavax, Sanofi and Medicago. Medicago is a bit of a special category, but I'll put it in that bucket as well.
If you're looking for more information on the differences between those technologies, I suspect that my health colleagues are better able to help.