Indeed. Unless they are grating the wasabi in front of you, you should assume it is colored horseradish. (Unless you're at a 2 or 3 Michelin-starred sushi restaurant in Japan- then it's real wasabi.)
Real wasabi is amazing. I live in Shizuoka prefecture, so I have ready access to it. In Japanese they call it "hon wasabi" (or root wasabi). The taste varies considerably over the season, but in the winter it is especially sweet. I often eat it on its own (just grated) as an accompaniment to beer. It is not nearly as hot as the horseradish/mustard substitutes, though most Japanese people think I'm crazy until I invite them to try it.
In Shizuoka, anyway, hon wasabi is not so expensive. You can get a root from between $5-10 US. That's enough for probably 10 servings. If you are at any decent sushi restaurant/izakaya you will be given hon wasabi here. Even at cheap kaiten (conveyor-belt) sushi restaurants you can usually order it for a small price.
