No they are not the same thing.
Bentonite is an absorbent aluminium phyllosilicate, generally impure clay consisting mostly of montmorillonite. Bentonite usually forms from weathering of volcanic ash. Bentonite can be used in cement, adhesives, ceramic bodies, and cat litter. I don't think this is approved as a feed supplement.
Diatomaceous earth also known as DE, is a naturally occurring, soft, chalk-like sedimentary rock that is easily crumbled into a fine white to off-white powder. Diatomaceous earth consists of fossilized remains of diatoms, a type of hard-shelled algae. Natural freshwater diatomaceous earth is used in agriculture for grain storage as an anti-caking agent, as well as insecticide. It is also approved by the USDA as a feed supplement.
It is also used as a neutral de-wormer. Some farmers add it to their livestock and poultry feed to improve the health of animals. "Food Grade Diatomaceous Earth" is widely available in agricultural feed supply stores. It is acceptable as organic feed additive for livestock.