The answer is "some does, some doesn't". The turret tooling interchanges (hope that's obvious). The head-mounted slides are not compatible, so you can't use the ASM head-mounted forming or cutting toolholders on the DSM slide. I believe (offhand, not certain) the cross-slide heights are not the same, so the direct-mounted tools (like the multi-tool forming toolholders) have different versions for ASM and DSM. The cross-slide riser block would also be different heights.
The Yahoo Hardinge lathe/mill group has brochures for the ASM and DSM, and you can compare the available accessories for the two machines. Sadly, Hardinge did not give the actual part numbers for all the accessories, so sometimes it's not explicitly clear whether the two machines take the same, or just similar, parts.
Larry Vanice can probably give you the authoritative and comprehensive answer.