According to the Collins dictionary:
If you trip when you are walking, you knock your foot against something and fall or nearly fall.
Stumble: to trip or fall while walking or running.
They seems to be synonyms. Are there any differences?
Compare these two sentences below, I don't see much difference.
He tripped and fell.
He stumbled and fell.
As is the case with many synonyms, these two words have overlapping meanings but they don't always fully align.
In your example, I wouldn't use trip unless he caught his foot on something, and that caused him to lose his balance. But there are other things that could cause stumbling besides tripping over something.
For example, if someone was stumbling because they were drunk, but hadn't tripped over the curb or something, then your second sentence might be a better option than your first:
He had had too much to drink at the bar. He staggered outside, then stumbled and fell.
Interestingly enough, NOAD defines the verb stumble as:
stumble (v.) trip or momentarily lose one's balance
