DX10 is basically becoming DX11, you'll run DX11 but it will only use whatever features your card is compatible with. ITs like a program supporting SSE4 but you have an older CPU that only has SSE3, the program supports all the SSE versions 1-4, but will use 3 with that CPU, the software supports up to 4 though.
In gaming you also need a dx10 or 11(or inbetween) game, because DX9 is completely separate. On win 7/vista machine you'll have(or will have shortly) DX11 and DX9 installed. a DX8 game will use the DX9 code, and only use all the features in dx7 and 8 that are contained within DX9. If you have a DX10 game, you'll use the DX11 software, but again only the DX10 features. If you have a DX11 game, but a 8800gtx, you'll still use DX11, but again because the card only supports DX10 the software will only use features compatible with DX10.
So if you have Win 7, dxdiag should should DX11, vista should show 10 till you update to dx11, and it will show that no matter what card you have in the system.
XP obviously will only show DX9, even if you have a dx11 card in there(haven't checked that in years but should be true).