Do I have common or hybrid Bermuda grass?

Common bermudagrass will release a tiny yellow cloud of pollen on the paper. Hybrid Bermudagrass is sterile, it does not produce pollen. My personal observation is that if you can see the two growing near each other, the hybrid grass will have a deeper green color when compared to the common type.

Are there different varieties of Bermuda grass?

The Common Bermuda grass varieties are usually seeded varieties. Cheyenne, Jackpot, U-3, Santa Ana, Ormond and Yuma are examples of common Bermuda grass. Bermuda hybrid grass varieties include Tif varieties (such as Tifway-I, Tifway 419, Tifway-II, Tifgreen, Tifeagle) and Sunturf etc.