The difference is that “hand over” is a verb and “handover” is a noun. To be precise, “hand over” is a phrasal verb and “handover” is a compound noun.
So we say: He handed over the money on Saturday.
And: The handover took place on Saturday.
There are many of these in English, and they are particularly popular in business writing. Here are a few more:
selldown / sell-down
startup / start-up
takeoff / take-off
Note that some compound nouns are written as one word, and some have a hyphen (and some may be written both ways). Phrasal verbs are always two (or more) words.