When you run DOSBox, it emulates everything, so as far as Windows is concerned (or Linux, but that's not related to VDMSound much) it's just a "game", as it's using SDL->OpenGL/DirectDraw/D3D/etc.. When you run a DOS game without DOSBox, Windows runs the code on the CPU in 16-bit mode (as opposed to 32-bit, which most things run in) and emulates a few devices (as opposed to the whole machine, like DOSBox). This is why under "NTVDM" (the name for Windows's DOS capability) you need slowdown programs and such. DOSBox was designed for games (primarily anywho) while NTVDM was designed for business prorgams, so NTVDM does not emulate a sound card, as business programs don't need it. VDMSound emulates a sound card of the era, so when you combine VDMSound and NTVDM you get a DOS environment to run games in, but they still run on your processor, unlike in DOSBox, which emulates it. The only real reasons to use (or rather, to prefer, since they both do the same job in the end) NTVDM:
- Your machine is older, and can't run a DOS game in DOSBox at full speed. VDMSound + NTVDM may be faster.
- You need direct hardware access to a floppy drive, or other piece(s) of hardware. Microsoft made NTVDM, so it has the ability to delve into the internals of Windows for access to these things. DOSBox could be improved to do this, but can not yet (except for a select few things, like CD-ROM, and in some patched versions MT-32, and a few other things).
There are far more reasons to prefer DOSBox when running games, because like with the sound, NTVDM doesn't concern itself with other things that allow some games to run correctly (display emulation and CPU speed, primarily). Also you only get Sound Blaster 16 sound from VDMSound, and some games use other outputs which are available in DOSBox but not VDMSound/NTVDM combined.
I hope this clears things up for you, and if you have any questions I'd be glad to answer and explain further.