Most people don’t realize this, but the “wasabi” paste you get in a tube is usually common horseradish with a little green food coloring and Chinese mustard. The better brands may contain a little real wasabi, but are still mostly horseradish.
True wasabi (aka wasabia japonica, Japanese horseradish) is a greenish rhizome (root-like stem) that has a milder bite than horseradish and is full of nuanced underlying flavors. The difference in quality is such that the world’s finest sushi chefs will use nothing else, and true sushi connoisseurs love them for it.
Why is it so rare? Wasabi is a temperamental crop requiring very specific growing conditions and exacting care to flourish. It is also rather perishable. Because of these factors, real wasabi can be extremely hard to get your hands on.