Re: In fact, warning does make sense
Correct. Peanuts are, quite literally, a type of pea.
However, you can still be allergic to peanuts. And because they are called nuts, the warning is intended to include them too (buy anything with peanuts and it won't say "may contain peas", it'll say "may contain nuts".
Be suspicious, however, of anyone who claims to be allergic to "all nuts". Because most of the things they'll say they are allergic too aren't actually the same thing at all and it's incredibly unlikely that they are allergic to ALL "nuts".