There can be variances in size among different manufacturers, but the tire specs are published and you should have no difficulty finding another brand that would match yours ok. If you can't find the complete specs online for each manufacturers version of the tire, ask a dealer. Tire diameter, rolling circumference, revolutions per mile, tire width, dual spacing, etc. are all spelled out in the detail specs.
Duals ought to be the same diameter, within about 1/4", so that the circumference remains very close to the same. That means that you should not install a new tire with a worn one, since tread wear can make a difference in diameter too.
Width doesn't have to be the same as long as the width does not substantially reduce the space between tires. If yours are already very close, then obviously you can't use a wider tire, but in most cases there is adequate room and slight difference is not a problem.
Former owner of 2004 American Tradition and several other RVs
Home is West Palm Beach, FL