Can a MAC be used as a HMAC? I am reading through an information security book right now, and a confusing question poses itself to me:   

"Could you use a MAC as a HMAC? That is, does a MAC satisfy the same properties that a HMAC satisfies?"  

The book then goes on to give a hint about how MACs are computed by CBC mode of a given symmetric block cipher that involves K the key, and to consider when K is known to an attacker for both HMAC and MAC.  

Here's the confusing part: Isn't a MAC just a code created from a MAC algorithm, while a HMAC is a type of MAC algorithm? I do not see how any of these hints could be applicable to the question when a MAC and a HMAC are so clearly similar (to a novice). 

Am I right in this thinking?
HMAC is a type of MAC. The output of a MAC is called a "tag". Not all MAC (algorithms) are HMAC.

MACs are not required to be one-way or collision resistant for someone who knows the key. HMAC, however, inherits the one-way-ness and collision resistance of the underlying hash function.

A CBC-based MAC is mentioned as a hint because it is almost trivial to find preimage values for any given tag value. That also makes collision attacks trivial.