What was life like under Nazi rule in the Scandinavian countries? Was there a distinction between the way the citizens were treated there versus in other parts of occupied Europe?

Was there a distinction between the way the citizens were treated there versus in other parts of occupied Europe?

Yes. Then again there were differences between each occupied country so it's a "given" that the Scandinavian experience would vary. I'll keep the summary confined to Denmark as I know more about the topic; hopefully someone can offer a Norwegian perspective - it is, in many ways, more interesting (and dramatic) than that of Denmark, but it really deserves a expert to condense.

Denmark and the various forms of German States had a contentious relationship in the century prior to the Second World War. The "Slesvig Question" incurred two wars (or, if you're more cyncial, provided enough political cover for hostility) in 1848-1850 and 1864. Denmark suffered a humiliating defeat in the latter of the two wars at the hands of Prussia; the defeat influenced the way in which Danes approached the incipient concepts of "romanticism" and "nationalism" - two concepts that would, arguable, play a substantial role in later German aggressions in Europe (WWII, in a particular extreme). Danish nationalism developed as distinctly passive notion centered on a notion of insularity and as a rebuke of Danish involvement in Great Power politics in Europe (due, in no small part, to the fact that previous attempts from 1600-1864 resulted most often in calamitous Danish defeat - too often at the hands of the goddamn Swedes, but that's another story). This notion is represented quite vividly in the way in which Denmark handled the Slesvig Plebiscite and the close of the Great War.

In the Great War, Denmark was officially a neutral country, but certain elements of Danish society supported either sides. The urbanites and a substantial portion of farmers - Denmark was then a primarily agricultural nation and economy - supported the Allies either out of fear of German aggression or economic links between the UK and Denmark (...aka Danish bacon...ok, maybe a little more complex than that). There was another group of farmer, particularly those in the southern districts of Jutland, that made substantial sums of money provisioning the Germans with foodstuffs, particularly canned rations (which were horrid concoctions of various kinds of meat, crushed bone, detritus, whatever could be condensed, canned, and shipped). This earned the name Gulash Baroner (Goulash Barons) in Denmark and they would assume a nouveau-riche social role in the interwar period, but were derided in no small part for war profiteering.

So that's a brief cultural background of Denmark prior to the Occupation: passive, insular nationalism, content to remain to free from European entanglement, but also economically connected to (and willing to profit from) belligerent parties in Europe. Hitler's intention in occupying Denmark had little to do with the country itself. The Germans wanted to control Denmark as a stepping-stone for their invasion of Norway, which they sought in order to secure German access to naval routes in the North Atlantic and to secure the flow of war materiel from neutral countries like Sweden. There is however, a wrinkle in all of this that confuses the way many interpret the Danish occupation. Nazism borrowed liberally from Nordic cultural heritages in crafting their ideology and many Nazi ideologues (most famously, Himmler) had a peculiar love of Nordic cultural traits. The Danes (and Scandinavians in general) were "Aryans" as conceived by the Nazis, but that did not mean that Denmark or Norway was occupied in a gesture of brotherly Aryan sentiment or that the Danes and the Norwegians were treated differently because of their supposed racial similarity to Nazi ideals. Overtures to that effect were certainly made by Nazi officials, and some Nazi administrators certainly believed in a notion of Aryan brotherhood, but Denmark was occupied for strategic reasons first and foremost.

We have to remember that, as much as Nazism purported to be a racial ideology, it was solidly enmeshed in German cultural traits. The occupied Danes and Norwegians did not view their Nazi overlords as benevolent, friendly, or culturally similar. They were, in short, Germans and thereby distinctly non-Danish.

However, Denmark was afforded a degree of autonomy abnormal of other occupied territories. They were allowed to retain their national parliament and domestic political institutions for a time, but that policy was largely a result of the lack of conditions that would warrant stricter German control. The Danes were conquered within hours of German's breaching the southern order and, outside of the Danish navy scuttling its fleet, no major battles or engagements would take place within Danish territory. There was little need for Germans to exert control, the Danes understood fully where they stood in the power-relationship between Denmark and Germany. German soldiers, for their part, considered a posting to Denmark to be serendipitous - the nickname for such an assignment was (I believe, don't have the source right in front of me) "the whip-cream front" (flødeskumsfronten)

The early years of the occupation were relatively uneventful, but still a traumatic experience for the Danes. The farmers that had previously found profits in selling to the German military established were cut out of the trade by German confiscation of agricultural produce, Denmark suffered the same loss of materiel as experienced in other occupied countries. There's an oft-repeated myth that the now-well regarded Danish bicycling culture originated in the occupation, but that is demonstrably false. Rubber, steel, pretty much any of the materials needed for owning and repairing a bicycle were redirected to supporting the German war effort - getting a flat tire in occupied Denmark meant, essentially, that your bike was now useless. As such, bicycling (along with many other normal elements of Danish life) was suppressed by a the shortage of goods created by the War - it was in fact the streetcar that conveyed the majority of Copenhageners during the war, fwiw.

At a personal level, Danish citizens were renowned (or infamous from the perspective of a German solider) for the "cold shoulder" - that is to say the Danish response to occupation was to essentially refuse to acknowledge the presence of Germans. The Nazis did support Nazi-inspired groups in Denmark, but they never gained the political power afforded them in other occupied countries - again, mostly due to the German desire to not actively micromanage Danish affairs and due to the countervailing Danish conception of nationalism which considered Nazism a German inventions and thus Danish Nazis were traitors to their own "nation".

Sabotage and resistance activities were rare at first, but gradually increased throughout the occupation. As the German war effort faltered in Russia and its previous unassailable position in Europe seemed vulnerable, the occupation tightened significantly within Denmark. Industrial facilities and infrastructure were blown up regularly by Danish saboteurs, illegal newspapers began to appear, and the utter failure of German authorities in capturing the Danish Jewry - or rather, Danish resistance to the attempt (fascinating back-story to this, but warrants an independent post) resulted in the occupiers dissolving the Danish political institutions (and detaining the Danish police forces) and instituting an occupation more similar in style (though not nearly as severe) to other occupations throughout Europe. It did not, however, end the sabotage which continued with increasing frequency throughout the latter-days of the occupation. There were counter-resistance groups in Denmark, most infamously the Schalburg-Korps - a paramilitary organization of Danes that conducted reprisals raids (known as "Schalburtage) and assassinations of Danish resistance figures.

Ultimately, the occupation ended with a whimper rather than a bang. The Danes were officially relieved by the British, but the German retreat from Denmark was rather ordinary (there is a famous photo of a retreating German soldier packed to the gills with cakes, bread, and general Danish agricultural produce).

Now, there's another question that OP doesn't touch upon, but I think is very interesting and I have a few extra characters left within the limit. There's a sense in the US (where I grew up), or rather penchant, to be more forgiving of German actions in the war - drawing a harsh line between Nazism and German nationalism. That is not the case in Denmark (where my father is from); Danes considered Nazism and German nationalism to be inherently related. Perhaps they weren't identical, but the general Danish post-war sentiment was that the German populace knew exactly what Hitler was proposing, supported it, and exerted it on Denmark and across Europe. My father is much more reluctant to forgive Germany of the taint of Nazism than I was or was taught in school (granted, my grandfather participated in the resistence, was military engineer in the post-War era, and had an unshakeable hatred of Germany and Germans in general, so there's no small amount of personal bias). I can remember distinctly watching that movie (I can't remember the name) about the Danish rescue of the Jews; there's a scene where the protagonist is leading a group of Jews to the coast when they're spotted by a German patrol, but let pass without incident. My father huffed and puffed at that, "they would never have done that, the Nazis (read: Germans) would have murdered them then and there". And that's just one instance; he claimed when Germany won the WC a few years back that he was happy the best team won, but that he could never support a German team (but that he was happy my generation could live without that baggage).