Or are they two completely different incompatible things? Are they at least the same size/scale?
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Primarily the base is different. D&D miniatures are 25 mm with bases that are ideal for standard battlemats. Heroscape are about 32 mm with bases designed for hex pieces and so they are a little too big for standard battlemats.
If you are okay with the overlap they can work (we use them as my son has a ton of fantasy themed Heroscape). For larger monsters they sometimes work quite well.
The good news is WotC just shaved off 2mm from the base (starting with D2, the Eberron set) which makes them equivalent to D&D miniatures. Even though the bases will be the same size they will still be different in composition.
Correct, Wave D2 was recently released, not surprisingly with a D&D theme, and has a smaller base to make them more D&D friendly. All previous sets had bases that were a little large but in practice, seldom caused a problem as long as I avoided using too many of the in confined maps.