Any DOT tire can legally be used on the street...so basically any tire that is not a slick or marked for non-road use only is a DOT tire.
As with regular street tires, they are manufactured with different criteria in mind....longevity, grip, heat cycles and so on. Hence each manufacturer has a wide range of street tires for different applications (even for the same type of bike).
The closer you get towards high-performance riding (track), the more focused does the tire need to become (usually focus is on grip rather than longevity). This allows the usage of softer compounds with different heat characteristics. The in-between tire is usually the specifically marked DOT tire...it has a softer compound (most even have different ones to select from), works best at higher temperatures than a street tire and is more affected by heat cycles (hence you usually want to run warmers on them). While you can legally use them on the street, you usually cannot keep enough heat in the tires to make them work their best and hence manufacturer label them as track tires.
Hope that helps...