But also, outside of Japan, 95% of the time the stuff with your sushi isn't wasabi, it's green-colored horseradish-and-mustard paste.
so unexpected that i had to look it up; turns out you're right: https://chefcoca.com/blogs/food-service-equipment-resources/...
Wasabi and horseradish are different! Horseradish is used as a substitute for wasabi so widely that you definitely can get the impression they are the same. But they are different plants.