Wizarding Law is both much simpler and much more complicated than muggle law.
Originally magical law was a loose set of rules and guidelines created by the Wizards' Council as a complement to the Law of the Realm – be it king or queen or a local warlord. For the most part it outlined punishments for forbidden magics such as demon summoning and treasonous acts such as betraying one's lord. There was no jury and no lawyer – the evidence was provided to the Council's Wizengamot and it sent out the Snatchers to mete out the singular irrevocable punishment - death. No appeals, no takebacks, no prison sentences.
When the Statute of Secrecy forced the magic users into forming a more structured and detailed Ministry of Magic, the magical law enforcement was forced to manage a set of basic laws formerly created and enforced by muggle authorities, in addition to expanding to deal with petty and accidental breaches of the Statute of Secrecy, as well as an ever increasing list of things that needed to be taken care of – such as hiding and tending to magical creatures, protecting centaur hunting grounds and goblin caves, erasing memories of muggle witnesses...
Harried and forced to adapt to changing times Ulick Gamp, the first Minister for Magic, founded the Department of Magical Law Enforcement on the basis of three simple principles – protect the Statute, protect the wizards and punish illegal magics. To deal with the varying severity of the crimes, he had to introduce the concept of fines and prison sentences. It is for later purpose that he acquired the infamous prison of Azkaban.
As the wizarding justice evolved the DMLE had to expand from the original two divisions (Wizengamot as judiciary and the Auror Office as the enforcement) and incorporate an ever-increasing number of sub-departments to deal with lesser law-breakers – from Improper Use of Magic to Misuse of Muggle Artifacts. In this manner the DMLE and magical law progressed for the next three centuries – reactive rather than proactive; a set of simple laws with a never-ending array of strange and unique precedents.
I'll skip over the anti-muggle sentiment as well as goblin and werewolf rebellions that colored the time and created a rather unpleasant trend in society and law, and skip straight to the modern day structure and difficulties of the Wizarding Law.
The first thing one must realize before entering the treacherous and ever-shifting landscape of justice is that law and politics are firmly intertwined. This is a good news for you if you are a regular person that never involved himself in politics and found yourself breaking the law in some minor way – as long as you didn't kill somebody or didn't use an unforgivable, you will probably get away with a fine (do not call them bribes) or maybe not even that if you spent a few days with the books and found some kind of a suitable precedent (and there's a precedent for pretty much anything). In a world where making people grow antlers does not constitute an assault and love potions do not equate to drugs, magic blurs the lines and dulls the edges of any infraction.
On the other hand, if you have insulted or hexed a politician, if you work for a politically inconvenient radical or publish politically inconvenient statements, if you are fiscally supporting someone pushing a law through the Wizengamot – then you are in trouble. Your best bet is to find yourself as many allies in the higher circles of the government as possible and hope for the best since you will indubitably be judged in front of the entire Wizengamot for even the most innocent of crimes and most clearcut of cases.
The second fact of Law may seem rather contradictory to the first, yet it is the undeniable truth that the Wizarding Law is static and unchanging. To better understand the seeming contradiction one must first understand the nature of the entity that is Wizarding Britain (or, really, any othe country with a large wizarding population). For the purposes of the explanation. I am terming "Wizarding Britain" as the magic-using human population that inhabits the boundaries of the British Isles. As there is no single census for every witch and wizard in Britain, I am mostly using the directories of Hogwarts and other British magical schools in conjunction with the records of O.W.L.s and N.E.W.T.s kept by the Wizarding Examination Authority.
A wizard does not need other wizards to survive. He is fully capable of acquiring shelter, food and water with only an Acceptable in Charms and Transfiguration O.W.L.S. And everything else can be acquired from muggles through either legal means or a combination of confounding and memory erasing charms (please note that the book does not support such practices, but I'm realistic enough to realize that MoM lacks the means, the will and the personnel to enforce the ban). The role of the Ministry in the life of a regular wizard is to provide protection and entertainment (the reason why Daily Prophet and other publications such as Quibbler focus on sensational or amusing stories and favor over the top reporters).
The population of Wizarding Britain is around three thousand – really, just enough to fill a single town. Wizards and witches however do not live together with the exception of Hogsmeade, but are spread all over the country living either among muggles or by themselves. Most of them never really interact with each other outside of old Hogwarts friends and Quidditch pals, their only real connection to the greater community is the Daily Prophet. The only people who interact with those outside their close circle of friends are those who work for the ministry (about 20% of the population), a school (less than 5%) or in Diagon Alley (10%, 15% if including part-timers). These people work for political power, social connections or money for luxury goods. The remaining 60% are either old enough, rich enough or lazy enough to survive with little to no contact with the general community.
These people don't care about politics, they don't care about the muggle world, but they will push back against any attempt to change their lifestyle, against anybody saying "hey, isn't it kinda wrong to obliviate muggles to leave a house so you can settle in?" or "hey, isn't that kinda harsh to kill your house-elf for burning your breakfast?" When faces with criminal cases they want a black and white picture since they can't be bothered to find out all the facts and figure out the gray areas.
Hence the static and unchanging laws, hence the blatant difference between small fine and the hell-hole that is Azkaban.
The third and final fact of Law is that Quidditch trumps everything. Yes, everything.
I could try to explain that Quidditch is the epitome of entertainment that is so important for the general population, I could give the example of Ludo Bagman who was let go without even censure in his files for giving information to Death Eaters while Rookwood was sent to Azkaban for life for that exact same crime, I could try to make parallels with the influence of Olympics and the World Cups in the muggle world, but sod it, not even that is enough to explain it. It's illogical, it's bizarre, but Quidditch has a magical gravitational pull of its own and even the most powerful of politicians do not dare stand in its way.