Here's what I call it. Not sure how others would.
If a team NEVER plays a game that season, there is no result. Game never existed.
If a team plays at least one game that season and cancels a game for any reason AND I'm not able to replace that game, it counts as a FORFEIT win for me and a loss for the team that cancels. If I replace the game, then the original game never existed and the results of my replacement game will determine if I have a win or a loss that week. (Replacing it in your original bye week is the same thing; as far as TAPPS and UIL are concerned, you can only play 10 games in the 11 weeks of the season.)
Not sure how it works in UIL land, but as far as TAPPS is concerned, I believe that a forfeit in a district contest cannot be replaced by another game. That means if a district team forfeits and the game counts for district standings, I can't replace it with another game, because then I would have two games that week (the forfeited win and the result of the added game).
Compensation would be determined by (1) any agreement or contract between the two teams and/or (2) any league or district rules if it was a contest governed by league rules. TAPPS started to require in 2012 that ALL VARSITY FOOTBALL -- district or non-district -- be done by written contract. I think they also require that games (in all sports) against out-of-state teams must meet some requirements (primarily that the opponent be a member of a state association).
About 10 years ago, I remember reading an editorial about how one of the big West Texas 5A schools got snookered by a Louisiana school for a "home-and-home" deal, nothing in writing but the first year of the deal was in Louisiana and supposed to have out-of-state refs (neither Texas or La.). When the team gets to Louisiana, the Texas coach notes that the officials that showed up were locals and he tells his opponent that next year, when they come to Texas, he'll hire Texas refs. The home coach then tells him (just prior to kickoff) that "we're not going to Texas next year."
While others might have other opinions, I always went by the rule that if you had enough kids in uniform to play the game (name the sport), you played the game. It might not be the six kids you want to play, but as I've said ... if Tony Romo is hurt, you don't see Jerry Jones calling up about rescheduling the Cowboys game for next week.
Your mileage may vary. Consult your doctor, attorney, or other professional before relying on this information.