The consumer surplus is the excess value the buyer receives. Think "I would have paid €5 for that drink right now, but they only charged me €2!"
The producer surplus is how much more someone paid than the producer was willing to sell it for.
The same thing can be worth different amounts to different people. Airlines in particular are good at price discrimination: trying to extract as high a price as possible, capturing the possible consumer surplus. Universities too.
Lots of things get no-haggle prices that ignore this difference between price and value.