The list is much longer than the examples I have supplied. Does this discrepancy between layperson's terms and botanical terms really matter? For the layperson, no, of course not. It is fine to eat your "nuts and berries", oblivious of how they are classified by botanists. Perhaps to differentiate between what is a seed and what is a fruit, though, is important, especially if you want to plant one.
For those interested in botany, the more formal terms provide quite good classification knowledge, which helps to predict the structure of the fruit of a particular species or genus.
It's common for scientific or professional terms to be part of a more complex hierarchy than a layperson's terms. It's not practical for these differing terminologies to merge. Botanists, for instance, use their specialist knowledge and understanding of fruits amongst themselves but that's not a good reason to relabel a packet of peanuts. Never the twain shall meet.