You can Loft Fly all pigeons. That means releasing them from your loft and let them fly around. All can be trained to come back into home loft. Homing pigeons are the ones that can be released from far distances and they find their way home. Usually the longest distances (races) are 600 miles.

... It is possible for pigeons to come from farther distances.
Birmingham Rollers, and tumblers can be trained to return to a Kit that is a portable cage. You take them to a park and release. The training is quite intensive, but you can train them to come back to your cage. Then you pack them back into your vehicle and come home.
Similar with High Flyers. You take them to competitions in a Kit, and they return to it.
I never had any of these pigeons, although I do want to get some High Flyers. Rollers,,,,,,, I have no interest in

The above 2 varieties will not make it home from far distances.
I am not sure how far they venture on their own when loft flying, but they usually don't go very far.
You can also hang out on the Pigeon Bulletin Board. Much useful reading there also.
https://www.backyardchickens.com/threads/pigeon-bulletin-board.1174207/