What I call a voxel is much smaller (on the order of a screen pixel), and drawn as a point sprite or screen-facing quad with a single color. Texturing is achieved by having many voxels with different colors/materials.
Here are some videos of what we used to call voxels:
DOS game: https://www.youtube.com/watch?v=51E_G7NCXVM
Gameboy game: https://www.youtube.com/watch?v=3zVy-4CEFQU
Medical imaging: https://www.youtube.com/watch?v=GrLqFNhVL68
Note that they were not using voxels because they had a certain artistic style to them. They used voxels because with the hardware they had, this was the most realistic rendering they could achieve. Once GPUs came out with hardware-accelerated triangle rasterization, voxel engines died.
For more information about point-sampling, see this classic paper, "A Pixel Is Not A Little Square":
http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf
And for a more in-depth discussion of sampling, albeit in one dimension, watch Chris Montgomery's video "Digital Show and Tell":