[Beatrix]

How do we differentiate between the two?

Thanks Susan, I know you'll give a great answer!

[susan53]

It's the same answer as i gave to your question on shocked etc. Impressed is a past participle that can also be used adjectivally. And when this happens the word can always be followed by by - because of its passive implications :
His answer impressed me.
I was impressed by his answer.

But as an adjective its also part of a small group of adjectives which express a personal, evaluative reaction of pleasure or displeasure. Compare:

I was not very happy with his answer.
I wasn't really content with his answer.

So many participle adjectives which express this sort of pleasure/displeasure can also be followed by with as well as by :

I was not very impressed by/with his answer
I was not very satisfied by/with his answer.
I was not very pleased by/with his answer.
I was a bit disappointed by/with his answer.
I was thrilled by/with his answer!