Wasabi is called ‘Japanese horseradish’ but is a different plant (Wasabia japonica). However, if you eat wasabi sauce outside of Japan, chances are your sauce was made with horseradish! Both are part of the same family (Brassicaceae), but wasabi plants are fussier to grow and require cool, damp conditions to flourish, so they will struggle in dry zones.
By contrast, horseradish is more easy-going and so it makes a fine stand-in (coupled with mustard) if you are interested in Japanese garden ideas and you’re keen on wasabi flavors in your cooking.