1. in the process of sth
To 'work on' something means to spend time in order to produce or improve something. If you say you are 'working on it' it means you are in the process of doing something or trying to complete it. If you 'work on' someone, it can mean you are trying to influence them in some way, usually to sway their decision or opinion on something.
2. sth related to the workplace
a working relationship/model/session
If something is 'working' it means it is functioning or is able to carry out the task it was intended to. A person who is 'working' is someone who is employed or engaged in work of some kind. As a prefix in 'working relationship/working model/working session' 'working' in these contexts refers to one of these two meanings.