They are both members of the brassica family, which includes cabbage and similar vegetables, but also strongly flavoured plants used in food flavouring, such as horseradish, mustard and wasabi. In fact some people call wasabi Japanese horseradish, although it isn't from the same species as the horseradish and the taste is closer to that of mustard.

Unlike either mustard or horseradish, wasabi takes a long time to grow and doesn't keep very well, so fresh wasabi is expensive and needs to be used more quickly than most condiments. It is more often used in powdered form, which is still quite expensive if it's the real thing (some European outlets sell a form of cheap 'wasabi' which actually has a lot of horseradish in it). Powdered wasabi will keep longer. It has an extremely hot, strong taste, but this fades after a few moments and unlike other strong condiments it doesn't leave a taste of burning in the mouth.