What's the difference between trapdoor and encryption? Trapdoor is a function taking as input $x$ and givings us output $y$ where it is hard to convert $y\rightarrow x $ back without knowing a secret $s$.

I think that $y$ is an encryption of $x$ under a some certain key($s$ or its associated public key).

So is trapdoor encryption?
A trapdoor function doesn't have the security requirements of an encryption function. If you directly use a trapdoor for encryption you open yourself up to related key attacks, known plaintext attacks, malleability  attacks and a whole host of other attacks.

Trapdoor functions are used as a single piece of a larger encryption function that handles all these issues.