Close relatives of the horseradish include woad (the ancient indigo source), turnips, rapeseed, cabbages, weeds (thale cress) and flowery shrubs & al. "Close relative" is not an indication of "not a lot of difference". You might as well say that mustard (also a close relative) is no different from wasabi.
You may well be right that there is no big difference between wasabi and horseradish, but them being "close relative" is not an actual argument for that unless they're much closer relative than just being in the same taxonomic family.
I didn't pick anything, I just looked up what the qualifier you picked meant. They're not the same species, they're not the same genus, they're the same taxonomic family, which also includes all the stuff I listed in my original comment.
>There's not a lot of difference between real and fake wasabi. One is horseradish and the other is a close relative of horseradish.
There was no strawman. Being a close relative does not imply "not a lot of difference."