If you look at this image, the easy answer is no. There are a different number of pin / pin arrangements
Now for the dificult answer.
Type A supports HDTV, EDTV and SDTV.
Type B adds the support of Dual-link DVI, although it has not officially been used yet.
Type C Mini is cross compatable with Type A, but a compressed connector for portable devices.
Type D Micro is the same as C, but it shrinks the head down even smaller resembling something like a USB mini connector.
Type E is used in the Automotive application.