There is a straightforward terminological clarification here, and then a much richer philosophical problem beneath it.
An "agent" in this sense is someone who does things. It derives from the Latin word "ago" which means "(I) do." Romans used it as their general "doing" verb for a wide range of activities. Our word "agenda" comes from the same word, and literally means "things that ought to be done." A secret agent is just someone who does things secretly.
A "moral agent" is therefore someone (or something) capable of doing things rightly or wrongly. Typically, this is understood to mean acting with the ability to freely choose (within parameters) what to do. It sometimes also includes the idea of being aware of the concepts of rightness and wrongness, or of what actions are considered right and wrong.
"Agency" is simply the capacity to be an agent, which means the capacity to do things. We see the same relationship between the words "regent" (a monarch) and "regency" (the commission to serve as a monarch or status of being a regent). Moral agency is the capacity to act as an agent. It's something that every moral agent has by virtue of being one.
Once you get the definitions sorted out, I don't think there's anything puzzling there. However, embedded in your question is a challenging question about who or what does the causing when a person acts. Does a person cause his/her actions? Is there some sense in which his/her agency could itself be the cause? This slides us into the longstanding problem of mental causation. It's the problem of how a mind (which seems at first glance to be a non-physical thing known to us through our conscious experiences, thoughts, and feelings) could ever serve as a cause of physical things like our picking up a rock and throwing it. It's very difficult to figure out what could be doing the causing when an agent acts. Given your interest, you may want to read more about mental causation.