In transparent mode, the proxy intercepts outbound port 80 connections and processes it. it creates a new connection to the real server. this connection uses the external interface ip adress as the source ip of this connection.
this way the original ip address of the client can not be seen on the real server.

Full Transparent does exactly the same thing, but it replaces the external ip adress on the connection to the real server with the original ip address of the client.
this way the real server knows the original ip adress of the client.

But this feature only works properly in bridge mode, as the real server will try to send the response back to the original client ip and if this client ip is not routable, than it does not work.

If properly used in bridge mode, the full transparent proxy is nearly undetectable.

I hope this is understandable
regards
Gert