As I recall, in Minecraft a voxel is defined by its position in space (x,yz) and a material - it is of fixed size and shape.
In DU, a voxel is defined by a position in space (x,y,z), a material, and a (1) vertex whose position relative to the voxel position can vary within a restricted range.
(Note: this explains why a core is seen to have one less "voxel" than advertised - it takes two voxels to define 1 edge [3 to define 2 edges etc.]).
What we see in voxel systems is defined (in part) by the vertices whose voxels have a material defined and also border those that have no material (sometimes called air voxels) - so interior voxels (those surrounded by voxels with a material) are never rendered.
The primary reason for using voxels is that they allow "real-time" modification (changing the material or vertex position) of a voxel which is readily rendered. In particular it allows "destructability" used in terraforming (mining) and PvP.