What is the difference between 几乎 and 差点儿? Recently I've studied these two words: 几乎 and 差点儿. My book says that they have different meanings and they are used in different contexts, however I don't quite grasp in what way they are different, even if I've been provided with loads of examples.

My teacher mainly focused on the meaning of 差点儿. According to her, this word have a slightly negative connotation, it indicates lack of something.

Maybe 差点儿 is more colloquial (口语)?

What do you think? Is there a clear difference between these two words?

Thank you!
差点儿 is more emotional. 

我差点儿迟到了。 implies that I feel lucky I was not late and I would feel bad if I were late.
我几乎迟到了。  states a fact and sounds like it's not a big deal even if I was late.

Visualize such a scenario. I run across the road and a car nearly hits me. My girlfriend says 你差点儿就被撞了！ It's a blame but I can feel she's really worried and feels grateful I was not hit by the car. I would be really sad if she says 你几乎就被撞了。