They give you a root, and a grater. Tastes milder than what we get, here.
I have heard that it is impossible to domesticate (has to be harvested wild, on certain mountains). However, I watched a program, where a guy in Hawai'i said he'd figured out how to domesticate it.
Haven't heard much about that, though.
Here is a decent paper that discusses the challenges[PDF]:
https://www.skagitmg.org/wp-content/uploads/Public-Pages/Foo...
To have it the spiciest you should wait a good ten minutes or more, the spiciness is activated by the process: "The chemical in wasabi that provides for its initial pungency is the volatile compound allyl isothiocyanate, which is produced by hydrolysis of allyl glucosinolate [...]; the hydrolysis reaction is catalyzed by myrosinase and occurs when the enzyme is released on cell rupture caused by grating" (adapted from wikipedia)
You can taste the difference but in most contexts it is pretty substitutable with the fake wasabi, hence the ubiquity of the latter.