You started from the wrong premise. Models and connections are two completely different things (why would there be different sections in MySQL Workbench if not?).
Via connections you can reach a server and work on it. Create users, retrieve data, create db objects etc.
Modeling is however the task to design a database structure. All the objects you create only exist within that model. You can design your structure from a higher level of view instead of going down to the pure SQL (which you can too, if you want). Nothing reaches a server until you either forward engineer your model or synchronize it to that server. The first is simply creating all the objects as you designed them, the latter is a two-way 'merge', that is, a diff is generated between the model and the server content and changes are applied to make the structure on the server be the same as in the model and vice versa.
Understanding that fundamental difference answer all your questions above.