Signature algorithms are what you use create and verify a digital signature. Examples are RSA, DSA, and EC-DSA
Signature hash algorithms are the same as hash algorithms and are what you use to produce the hash value that you would sign with one of the above signature algorithms. Examples are SHA-1, SHA-256, SHA-512 and MD5
So if you wanted to sign something with an RSA 4096 key pair using a SHA-512 hash it would look something like:
hash = SHA512(<the data you want to sign>)
sig = RSASign(hash, RsaPrivateKey)
and to verify would look like
hash SHA512(<the data you want to verify>)
valid = RSAVerify(hash, sig, RSAPublicKey)
