A toplevel window is active if it currently is receiving keyboard events. (The window or a descendant has the X keyboard focus.) A widget within the toplevel is active if the toplevel is active, regardless of whether that widget has the input focus within the toplevel.
In an embedding situation, the client is the window that is embedded into an embedder. Sometimes also called a plug. (Note that the usage here should not be confused with the typical X usage of "client" to mean an application connecting to the X server. That is always referred to as an application in this document)
[ Should we replace client by some other term in this document to avoid the confusion? ]
In an embedding situation, the embedder is the graphical location that embeds an external client. Sometimes also called a socket or site.
A widget is focused if it receives keyboard events within its toplevel. This is without regard to whether the toplevel is active, and has nothing to do with the X keyboard focus.