Finland came out of WW1 as an independent country, having formerly been part of the Russian Empire. Part of this process was a civil war between Reds and Whites. The Whites, in part due to military aid from Germany, including German soldiers fighting for the Whites, won. A German prince was elected King of Finland (but abdicated before his coronation due to German defeat in WW1, and Finland became a republic rather than a monarchy). Clearly, there were close ideological and cultural ties between Finland and Germany. However, this was the old Germany, Imperial Germany. At least some Finns remained grateful for German assistance (and others probably the opposite). However, while this is an ideological connection between the countries, it isn't an ideological similarity.

Rather than follow Germany's post WW1 path of increasing conflict between Reds and Whites (e.g., the Spartacist uprising in 1919), Finland's path was reconciliation. While the Civil War remained a bitter and divisive memory - over 1% of the population had died, with most deaths being executions or in POW camps - much of what the Reds had been fighting for was given to the Finnish working classes. As Finland entered WW2, courtesy of the Winter War, propaganda from the Soviet government and the puppet Terijoki government aimed at getting Finnish workers to rise up against their capitalist oppressors failed dismally - Finnish workers had gained what they had been fighting for in the Civil War.

The Civil War, and their very Red neighbour, the Soviet Union, did leave a strong anti-communist residue. This was something they had ideologically in common with Germany. During the Russian Civil War, there had been Finnish intervention in Russian Karelia and Estonia, with dreams of united them with Finland into a "Greater Finland". While this was not successful, it also left an ideological reside - the ideal of Greater Finland - that could be seen as a parallel with German dreams of conquest to the east.

Beyond this anti-communism (of many, but not all) and fantasies of Greater Finland (held by some, not by all), there was essentially nothing in common between Nazi Germany and Finland. Apart from political differences, the Finnish economy - essentially agrarian - was quite different.

Finland did see German support during the Continuation War as very useful, but Finland was fighting for its own goals, not Germany's. Some Finns make a lot of "cobelligerent, not allied", that Finland and Germany were not allies, just fighting against the same enemy. The amount of cooperation was more than a mere "cobelligerent" just happening to fight the same enemy - and a greater level of cooperation was entirely militarily sensible. Finland did take actions that were not in Germany's best war interests, such as stopping their advance towards the Murmansk railroad (which remained open for the rest of the war) and not attacking Leningrad. The former was in response to Allied pressure (especially British pressure) and the latter to not poison negotiation with the Soviets later in the war. Both were already taking into account the possibility of Germany losing the war.

The Finnish right wing largely supported the creation of "Greater Finland", "Suursuomi", by the annexation of Soviet Karelia. Many, including many in the army, didn't support this (and, following the occupation of large parts of Soviet Karelia in the Continuation War, it turned out than many of the Karelians weren't keen on the idea either, to the surprise of the Finnish rightists). The occupation of Soviet Karelia should not be seen purely as a step towards Greater Finland, but also to obtain a better frontier for defence against the Soviet pushback after Germany fails to win, and to hold territory that could be returned to the Soviets in post-war bargaining. Some certainly considered Greater Finland to be the main goal of holding that territory, but many did not. In the end, Finnish defence of Soviet Karelia collapsed very quickly in the face of the Soviet offensive, and the hoped-for military and political gains didn't result.

As for the swastika, Finland adopted this independently of Germany (and earlier). This came about due to the Swede Eric von Rosen who gave Finland its first military aircraft in 1918 to start its air force; this came with the swastika which von Rosen had been using since the beginning of the century. While von Rosen had Nazi connections (his wife's sister married Hermann Göring), the Nazis might have independently adopted the swastika (supposedly before Hitler met Göring, who would have been the most likely route if it came from von Rosen). At the end of WW2, the Soviet Union pressed Finland to de-swastikafy its military regalia (but apparently missed the air force flag, which kept its swastika).