Many riders don’t like the dressage term “on the bit”. They feel it has a negative connotation because it conjures up pictures of forcing a horse into a frame.
This is how I like to think about it so I don’t get bogged down in semantics.
Physically, the dressage term “on the bit” refers to a round silhouette that occurs when you ride your horse from behind, over his back, through his neck, and into your hands. (And at that point the energy can be recycled back to the hind legs)
Mentally, a horse that is on the bit is “on the aids” and anything is possible within the next step.
So, a Training level horse or a hunter, for example, can be “on the aids” but not necessarily on the bit.
Dressage horses at First level and above are both on the bit (physically) and on the aids (mentally).