Do all dogs run in the same way?

When a dog runs with his back legs together and hops kind of like a bunny, it usually means the the dog either has arthritis in his back legs or hip dyspepsia. Mine is doing that now. I give him Tramadol for the pain and it has been working wonders. You should take your dog to the vet and find out why your dog is running like that. Medication may really help. Dogs don't have to be old to have either one of those conditions.

Well structured dogs all have a variety of ways that they can move there legs for forward movement. A trot, a gallop, a canter, a run etc. Some individuals for structural reasons can not move their legs in all of the patterns - which are typically done for various speeds of movement, but also impacted by experience and terrain.

My dog runs sideways because his back legs go faster than his front legs. Whenever he runs his back legs try to overtake his front half and his butt swings out.

Get his hips checked out.