[subject] + 差点儿 + [verb phrase] + (了)
[subject] + 差点儿 + 没 + [verb phrase]
差点儿 means "nearly": it came close, and then didn't happen. It goes after the subject and before the verb, and the sentence often ends in 了. 差一点儿 and 差点 are the same word.
With something you didn't want – being late, falling, forgetting – 没 changes nothing. Both sentences say you weren't late.
With something you did want, 没 matters. 差点儿没 means it only just happened; 差点儿 + 就 means it nearly happened but didn't.
For a hoped-for result, 就 is usually there to make the regret clear.
Both contain 差, and learners swap them. 差不多 is "about" with a number, or "much the same"; it doesn't say something nearly happened.
English "barely" also means "hardly at all". 差点儿没 never means that.