If this is your idea of connected to then that explains your confusion or why you think it is confusing.
Branch circuits are connected to the secondary of the transformer, if they weren't then we wouldn't have any power in our homes.
Take a few minutes to study Article 100. Maybe this will help clear your head.
The definition of ground be it past (ed) or present (ing) means earth
Ground. The earth.
Ground Fault. An unintentional, electrically conducting connection between an ungrounded conductor of an electrical circuit and the normally non?current-carrying conductors, metallic enclosures, metallic raceways, metallic equipment, or earth.
Grounded (Grounding). Connected (connecting) to ground (see definition) or to a conductive body that extends the ground connection.
But to an auto person it is the negative post of a battery. To moms it means go to your room. To electronics it means the chassis
All that matters to an electrician or inspector or even an engineer is what the NEC says in Article 100, the earth. The neutral is connected to earth thus it is called the grounded conductor.