What Topgun has said is true. Homing pigeons are usually on a mission, and that is to get home, so they are usually flying close to top speed. Barn pigeons usually are in groups and generally flying around in circles around a silo or such.
It is interesting to watch homing pigeons when they are let loose on either a training flight or a race. Most clubs have someone who will take the birds greater distances than you would drive to train them and release them and they will go to their respective lofts. Races on the other hand might have thousands of birds from a lot of clubs especially a 500 mile race. There are birds there that have been specifically bred and with special gold bands placed on them when young, and if these birds come in first, or second there is a lot of money won. The racing band is a piece of plastic with numbers on it and when the bird returns to it's loft and goes into the trap, the owner retrieves the band and puts it in a clock that records the time. Then clock is taken to the club when it is opened and the reading verified and the shortest time wins. They have all kinds of races, young bird, old bird, etc.
Like I said it is interesting to watch the birds released, all at once, they all group up, maybe a thousand birds, they circle 3 times only to get their direction and then head for home, flying up to 50+ miles an hour. On a long hot day race, it is possible some birds might stop for water, but not likely. Also there is a chance that birds could hit wires, get lost, confused, especially young birds.
A note if you ever find a homing pigeon that is lost, most times if you can corner it, you can catch it. Where I used to work before retiring, next to the Delaware River, birds use rivers for direction. I used to see a few homers and caught a few, took them home and nourtured them back and let them go home. Before doing so, take off plastic racing band, this way the owner knows that something happened to the bird and he won't kill it. If you let the bird go with the band on it, he will just think the bird went off and followed other racers, and then the bird is no good to him.
