[Editor's Note: This answer was provided by our table-games expert Dan Lubin, author of The Essentials of Casino Game Design.
What that does is it changes the house odds for a game or side bet under the same general rules and game feel for the player.
For the offerings on the Let It Ride Bonus bet, in the following chart, I've listed and highlighted the differing pay tables you mentioned.
This all is because individual casinos often want to tailor the house edge up or down and as a result, many paytables are offered to the casinos from which to select. Any of the paytables generally "feel" the same to the player while playing, as the bet wins on the same types of hands and near the same amount. Any paytable used by the casino must be in the group that's officially submitted to and reviewed and approved by the Gaming Control Board or Commission for that state or jurisdiction. Typically, game distributors add new paytables and/or new features over time to accommodate the market, based on what casino operators wish to offer.
However, over the time of a playing session (or many players and sessions), the house might discreetly take a bit more from, or conversely, give back a bit more to, the player, based on the paytable used. Highly competitive markets, like locals casinos, use looser pay tables for their more demanding clientele. Strip casinos use slightly tighter paytables, as they have more of a captive audience (unless visitors rent a car and are willing to travel out to the off-Strip areas, also an expense).
Let me mention here that the Bonus bet on LIR seems on the high side, but that it has to account for windfall payouts (like 20,000-1!), and explains why the bet is limited to a dollar. In a way, the LIR Bonus bet acts like a mini-progressive, which by its nature, requires a higher house edge, because the windfall payouts get "locked out." In other words, big winners return home with that kind of money, instead of re-betting it back into the game.
