ODPOWIEDZ! - English

So as is by now obvious, the words "drop" and "fall" have many meanings as verb, both transitive and intransitive, as well as being part of scores of verb phrases @ which they are assisted by any of several propositions to achieve different ends.

Drop out: quit, e.g., leave school before completion.
Drop in: visit someone/someplace (usually unannounced)

Fall + certain prepositions has myriad meanings...

Fall in (gather/assemble)
Fall out (dissemble/relax/recess)

Note: Both of the above, while having roots in military usage re; English, have become to be used widely among America's civilian (non military) as well.

And don't forget "to get the drop" on someone/something (e.g., a situation/development).

Drop a hint. (i.e., leave/offer a clue)
Fall from grace. (i.e., a decline in one's status)

Everyone has very nice explanations. Let me add it a bit. I think another difference between drop and fall is the meaning. Drop mostly means something that fall literally, and the size is usually refer to small things, at least smaller than human.

Fall is used for something bigger than human, e.g trees. Fall can also be used for something methaphorical like ’the fall of a civilization’