Difference between AES CMAC and AES HMAC?
A similar question as been asked before: Use cases for CMAC vs. HMAC?

To resume it, AES-CMAC is a MAC function. It can be seen as a special case of One-Key CBC MAC1 (OMAC1) which also a MAC function that relies on a block cipher (so AES in the present case).

HMAC is also a MAC function but which relies on a hash function (SHA256 for HMAC-SHA256 for example).

So the term AES-HMAC isn't really appropriate. If you read it somewhere, it could signify the process of computing a HMAC on the message you want to encrypt to ensure the integrity property (AES$[message ||$ HMAC$(message)]$ for example).

Note that there exists authenticated ciphers that simultaneously ensure confidentiality, integrity and authenticity.


  Also, does openSSL libs support AES CMAC and AES HMAC?


OpenSSL supports HMAC primitive and also the AES-CMAC one (see How to calculate AES CMAC using OpenSSL?)