@bear78-- Yes there are many varieties and they all look a bit different. There are some commonalities among the varieties as well. For example, most are vines with small white flowers. Jasmine varieties love warm/hot weather and they don't need a lot of water or shade. They tend to grow quickly and are often resistant to diseases.
Some varieties however have different sized flowers in colors like yellow. Some look less like a vine and more like a shrub. And the flowers may be larger/smaller with different numbers of petals.
But they're all very beautiful and look great in the garden or in a pot inside the home.