I chose the word envelope because I’ve always wondered if there’s a reason that it’s so close to envelop. Yes, these are the kind of thoughts that occur to me.
First of all, they are related. An envelope you put mail in came about in 1705 from the French (as in modern French, not one of the older incarnations) enveloppe. Enveloppe is what’s known as a back formation (more on that in a minute) of the word envelopper which means… “to envelop”.
English envelop showed up in the late fourteenth century as envolupen, “be involved in” from the Old French envoleper, the predecessor of the above envelopper. It is a combination of the prefix en-, which in this case means in or into, and the word voloper, which means “wrap up”, making it “wrap up in”. Totally fits.
Now as for that back formation thing. A lot of words are taken from other languages and modified, like we took envelop from Old French, but in a back formation, a word is formed by taking a previously existing word in the same language and dropping an affix. There are many examples in the English language, like destruct (a verb) being from destruction (a noun), or edit (verb) from editor (noun). In the above case, the Old French enveloppe it was taken from envelopper to be used as a word for something that envelops a letter.
TL;DR: An envelope envelops a letter.