Whats the difference between peppermint and mint? Same thing or not?

What about spearmint? What is " spear" actually?

As Wikipedia puts it: " Peppermint (Mentha × piperita) is a (usually) sterile hybrid mint, a cross between watermint (Mentha aquatica) and spearmint (Mentha spicata)." So it is a different species but from the same family.