something will happen
something will occur
A couple of thoughts:
In terms of syntax, 'happen', unlike 'occur', can function impersonally without a prepositional complement (typically with reference to events), thus
It so happened that a big meeting was held in the town that day.
but not
*It so occurred that...
while with one (with reference to thoughts/realizations), the situation is reversed:
It occurred to me that I had never seen them in the same room.
but not
*It happened to me that...
In terms of semantics, 'happen' tends to be more common than 'occur' with reference to daily events, particularly with interrogative or indefinite subjects, thus
What has happened here?
I waited all day, but nothing happened.
rather than
?What has occurred here?
?I waited all day, but nothing occurred.
although with reference to a weighty or problematic situation, the latter is often used, e.g.
"An incident has occurred, Prime Minister, requiring your urgent attention."
No doubt other contributors can supply some further differences!