DMOS is Double Diffused Metal oxide Semiconductor.
The cross section of a VDMOS (see figure 1) shows the "verticality" of the device: It can be seen that the source electrode is placed over the drain, resulting in a current mainly vertical when the transistor is in the on-state. The "diffusion" in VDMOS refers to the manufacturing process: the P wells (see figure 1) are obtained by a diffusion process (actually a double diffusion process to get the P and N+ regions, hence the name double diffused).
BCDMOS has
Very high voltage, yet small, transistors provide up to 250V Breakdown
Low on-resistance - just 0.6 ohm-mm*2 at 80V - allows integration of multiple low resistivity power FETs
Double metal layer supports currents up to 10A
Thin film and poly-poly caps are combined in silicon to integrate high-performance analog functions such as high-accuracy references, along with high-power devices.