PKI Encrypted hash vs Signing
The difference between encrypted hash and a digital signed one is twofold:


the key to be used for signature generation is the private key, so technically it is not encryption;
the padding scheme is different for both situations.


The use of the wrong key is already enough to not talk about encryption as explained in my Q/A here.

In the case of PKCS#1 v1.5, both encryption and signature generation are often referred to by the same name. However, both use a rather different scheme for the padding of the content (the plaintext message for encryption and the hash for signature generation).  For RSA v1.5, RSA encryption is called RSAES-PKCS-v1_5 and uses the EME-PKCS1-v1_5 encoding scheme. Signature generation is called RSASSA-PKCS-v1_5 and it uses the EMSA-PKCS1-v1_5 encoding method. Note that these names have only been introduced in version 2.0 from the specification.

The main issue is that the padding for encryption was designed to add a random component to the padding. This is required because otherwise identical messages would result in identical ciphertext, leaking information to anybody seeing both ciphertext. As it is random padding, it cannot be validated. On the other hand, signature generation uses a known padding which can be validated. This is important because you would want the unpadding to fail when verifying the signature in case it has been tampered with.

So using the wrong padding scheme means that the security premises of the RSA mode and padding are not valid anymore. This is one more reason why signature generation should not be thought of as encryption of a hash value. Both use the RSA problem to be secure. Practically speaking only the modular exponentiation is identical for both.