How do these two differ?
In general, loopholes aren’t cheating. They’re unintended consequences of the rules.
Loopholes are legal, albeit possibly ethically questionable, ways of getting out of something; cheating is against the rules, period.
I tried to explain this to my GF but for some reason she just wasn’t buy’n it. I can’t for the life of me figure out why. 
For instance, the IRS has the responsibility of setting up the tax code to get the money they desire. If an individual finds a loophole that allows them to keep more of their own money, that is not cheating. The IRS will penalize people and corporations to the letter of the code so individuals and corporations are under no obligation to go by anything other than exactly what that code allows them to do. If the IRS notices a lot of activity through that loophole, it is their responsibility to fix it.
True cheating would be things like not declaring income. There are different kinds of systems. There are those based on spirit of ideas and there are firm rule-based systems. Systems like families usually operate on spirit based rules. If you promise your wife you will never sleep with another woman, it isn’t good to find loopholes in that rule. Governments and big businesses however often operate under a strict, rule-based system. By doing that, they are attempting to control the whole system and others behavior. It is their fault if their system is imperfect. Also, you can’t always tell if a loophole is unintended. Maybe it was left their for good reason.
But, Sweetheart. We didn’t sleep. Honest!
I can see that defense working really well. :rolleyes:
If you were too drunk to remember, then it never actually took place…
Loopholes are the intended cheats built into laws because somebody with money wants them and his patsy in government can make them sound okay.
Say there’s a river-cleanup bill. Some offending company will pay for someone to sneak in a provision for “swapping cleanup credits”. Then the company will buy a neighboring company that has already installed effluent filters, trade credits, and come out needing to make no changes whatever.
With all the lawyers around, nothing involving money is accidental. Just they guy with vested interest is more inclined to know how the loopholes will work in practice.
Shagnasty calls it precisely accurately. A loophole is something perfectly legal which benefits you, an unintended consequence of how the law was written. For example, one of my wards, in his young adulthood, found that it was actually beneficial to him to claim more income from self-employment than he had actually made after expenses. There is (or at least was) nothing in the IRS code prohibiting him from not claiming expenses, or claiming a higher income than his actual net self-employment income was; the law is geared to prohibit not claiming all income which one actually received. Was it what he was “supposed” to do? Presumably not. Was it legal of him to do so? Certainly.
Smokey Yunick of NASCAR fame was perhaps the greatest expoiter of loopholes ever. He was also a superb cheat.
Back in the early days of NASCAR, stock cars were stock cars. Metal bodies with minimal changes. One of the changes was to take a torch and cut the rear wheels into a semi circle so that the racing tires could be changed easily. Like this . So at this one race ole Smokey shows up with a car that does not have cut wheel wells. This is both good and bad. His car is more areodynamic, and therefore faster. But pit stops will take longer. The other racers howl, and protest. Smokey’s response was a classic “The rules say I may cut the wheels wells, not that I have to.” His driver then takes the pole. Smokey proceeds to then cut the wheel wells to allow him to have quick tire changes during the race. The other racers again protest. His response? “The rules don’t say when I have to cut the wheel wells, just that I may.” That my friends is loophole finding at it’s best.
Now about cheating. From the Wiki link
(bolding mine)
Or perhaps the 7/8 scale Chevelle that he built. That lead to NASCAR requiring templates for car bodies. 
Correction. This should read Congress has the responsibility of setting up the tax code to get the money they desire. The IRS, like any other political fiefdom, gets the money it desires by petitioning Congress regarding its budget.