A placard is usually a sign held by someone (e.g. a protester) whereas a banner is more akin to a flag used to advertise something (e.g. promoting a business)

Banner is an oblong flag (e.g. banner bearer soldier) or oblong area on a website which contains logo or advertisment. Placard is a card like item with a sign or a name on it. (e.g. name placard, warning placard)

Yeah, Peter. I looked it up in the dictionary, but I wanted to hear native speakers' opinions:)

This is a question a good dictionary can answer. Have you checked your dictionary?