I understand that it gives the wrong impression, but I think it is not absolutely wrong, or is it?
It is actually. A hash algorithm computes a 'fingerprint' if you will of the input. So just as a fingerprint identifies you, a hash identifies the input document.
But just as an entire human being cannot be recreated from just a fingerprint, so the original document cannot be (easily) recreated from the hash. This is the fundamental distinction with an encryption. In encryption it's useful to decrypt, using the original encryption key. You can't with a hash, and it has no key.