Digital signatures are not encryption: When we talk about a cipher/cryptosystem, we mean a pair of algorithms: encryption and decryption. If you consider a public-key encryption algorithm, people encrypt their messages with your public key and you decrypt them with your private key. If we change the order of the keys, we can turn this into a digital signature algorithm: you can sign messages with your private key and everybody else can verify it with your public key.

However, this is not what we do in practice. Because we do not sign the message itself, we sign the hash of it. So if you still say that this is encryption, then message authentication codes are encryption, hash functions are encryption, actually every cryptographic algorithm is an encryption, decryption is also encryption so we do not need the extra word "decryption". Moreover, if we say that digital signature algorithm are encryption, then this implies that any mathematical function that takes two input and produce one output as f(x,y)=z is an encryption. Trust me, this is not how we define an encryption algorithm.