Click, as the name says by itself, is when someone has clicked on your ad, no matter is it a banner, crafted ad or any other ad. You will pay per click (PPC advertising).

Impression is simply visibility; how many times your ad has been exposed to, what we call, the right eye-balls, or your targeted buyer audience. But, in this case, you don't seek for sale but impression, you want something, an ad but not necessarily, to be seen. So you will pay to for example Instagram just for the impressions, to make your offer exposed, to raise your brand popularity or spread the awareness of your brand and so forth.