Tropaeolum majus is the genus and species of the commonly grown nasturtium you find in seed packets. I love it, and have it all over the place. It reseeds easily and comes back each winter here in zone 9b/ 10a. Some varieties are long vines and some are small and bushy. My favorites are Cherry Rose, Moonlight (a long vine,) and Creamsicle. Many of mine have crossed over the years so I have many others colors now.
There are many others nasturtiums in the genus that are perennial. Here are some:
Tropaeolum tricolor Bolivian Nasturtium
Tropaeolum speciosum Flame Creeper, Flame Nasturtium
Tropaeolum ciliatum Climbing Nasturtium
Tropaeolum tuberosum
Tropaeolum hookerianum
Tropaeolum incisum