The difference is subtle and not described in much detail in the RFC linked above in the question. The term "User Agent" and "Client" have a generic definition above how they are used in defining the HTTP specification.
A User Agent can be any software or automated process that acts on behalf of a User.
A Client can be defined as any software or automated process that performs requests for resources or services in a Client-Server model.
Essentially in a generic sense a User Agent doesn't necessarily require to operate in a Client-Server model. For instance, a User Agent might be an abstraction of a workflow software that automates a number of data processing steps on a work item based on defined business rules. It is performing this work on behalf of a User, although doesn't necessarily need to interact with a server to do so.
Essentially in the HTTP protocol, it is a network application protocol, and as such interaction between a client and server is a given. In this case they are defining the terminology of a User-Agent as being effectively synonymous with a Client. In the general sense for HTTP protocol they mean the same thing.