There are many many varieties of mint....those 2 are different....as is spearmint.

Chocolate mint makes you think of a York peppermint patty!

Common names do you no good, you need the scientific name. Here are some examples of scientific names:
Melissa officinalis, Lemon balm
Mentha x piperita, Peppermint
Mentha spicata, Spearmint
Mentha arvensis, Wild mint

On Wikepedia, I see Chocolate mint listed as a cultivar of Mentha x piperita. The "x" means it is a cross, and peppermint was a cross between a wild european swamp mint, Mentha aquatica, and Mentha spicata. Chocolate mint is a botanical cultivar of Peppermint. That means the breeders noticed certain peppermints with a hint of chocolate smell and bred those plants specifically. But it is not different enough from Peppermint to be a whole other species. Common names are easy for a lay person to use, but often don't tell you very much about the plant, it's origin or it's cultivation.

Here is a link that might be useful: Peppermint on Wikipedia

That would be "its" use and "its" cultivation, not "it's."

Oh, and BTW, I wouldn't be surpised if so called chocolate mints vary in the amount of chocolate smell and taste, AND, may become less chocolatey as the plant spreads in your own garden, and become more like its parent Peppermint. Smell and taste chemicals are greatly influenced by garden conditions, including soil, water and sun. Chocolate mint is a cultivar of peppermint, but it is NOT spearmint, Mentha spicata or apple mint, Mentha suaveolens.