Are mint and peppermint the same thing? Can we substitute one for the other. How can we differentiate between mint and peppermint? 
Peppermint is a hybrid breed of two plants belonging to the mint genus, spearmint and watermint. In my experience, when 'mint' is referred to by itself without any other descriptors, it usually refers to the spearmint flavour people are used to (from things like green restaurant mint candies, toothpaste, etc). Peppermint will be denoted as peppermint. However, as mentioned in the comments, this may vary based on region.  There is a significant difference in taste between peppermint and spearmint; I find peppermint to have a much more intense flavour. Scientifically, peppermint gets its flavour from its high menthol content, whereas as spearmint owes its flavour to the compound L-carvone. Substitution will not replicate the same flavour as the original.  Source for science related parts:  https://en.wikipedia.org/wiki/Mentha 