I'll premise this by saying that this is not my strongest area so there are likely going to be people who can provide a much more detailed answer. However, given my own area of interest, I do know a little bit.

In short, you're absolutely right in saying it was nuanced; although I'd probably call the situation chaotic. The history of the KPD, it's relationship with the SPD and fascism follows very closely what had been happening in the rest of Europe.

In the early to mid-1920s, the KPD's aim wasn't necessarily one of pushing for immediate revolution but pursued the policy of the 'united front' in order to win parliamentary seats, pursue social changes and counter the rise of fascism. This was not just a policy of the KPD but the explicit instruction given by the Comintern following its 4th Congress.

The Theses on Comintern Tactics contains very specific passages on what Communist Parties must do:

5. International Fascism

[...]

One of the most important tasks of the Communist Parties is to organise resistance to international fascism. They must be at the head of the working class in the fight against the fascist gangs, must be extremely active in setting up united fronts on the question and must make use of illegal methods.

One of the most important tasks of the Communist Parties is to organise resistance to international fascism. They must be at the head of the working class in the fight against the fascist gangs, must be extremely active in setting up united fronts on the question and must make use of illegal methods of organisation.

[...]

10. The United Front Tactic

There is consequently an obvious need for the united front tactic. The Slogan of the Third Congress, "To the masses", is now more relevant than ever. The struggle to establish a proletarian united front in a whole series of countries is only just begnning. [...] The Communist International requires that all Communist Parties and groups adhere strictly to the united front tactic, [...] For the sake of this struggle Communists are even prepared to negotiate with the scab leaders of the Social Democrats and the Amsterdam International. Any attempt by the Second International to interpret the united front as an organisational fusion of all the workers' parties must of course be categorically repudiated. [...] In the same way the united front tactic has nothing to do with the so-called electoral combinations of leaders in pursuit of one or another parliamentary aim. The united front tactic is simply an initiative whereby the Communists propose to join with all workers belonging to other parties and groups and all unaligned workers in a common struggle to defend the immediate, basic interests of the working class against the burgeoisie.

(emphasis mine)

As the KPD was at the time the biggest Communist Party outside of the Soviet Union, it was seen as the reference point and it saw itself as a leading example. Therefore, it adhered to the doctrine outlined at the 4th Congress of the Comintern and actively joined forces with the SPD on a number of occasions. This is not to say that it wasn't a frought relationship as there was still a certain level of distrust.

However, that did not last long as once Stalin consolidated his power and the Comintern came under his control, in around 1928, the policy of the united front was abandoned and Communist Parties instructed to actively fight against Socialist and Social Democratic parties. Stalin made some seriously scathing comments about the KPD, the united front tactic and Social Democrats at the 6th Congress of the Comintern:

The point now is that this situation in the German Communist Party cannot be tolerated any longer. The point is that to tolerate any longer an "order" of things in which the Rights poison the atmosphere with Social-Democratic ideological rubbish and systematically violate the elementary principles of Party discipline, while the conciliators bring grist to the mill of the Rights, would be to go against the Comintern and to violate the elementary demands of Marxism-Leninism. [...] we cannot deny that the Communist Party in Germany is still far from having rid itself of Social-Democratic traditions, which foster the Right danger in the C.P.G

(The Right Danger in the German Communist Party, also in Stalin's 'Works')

It's actually around this time that the term 'social fascist', a term which actually first appeared in Germany, was starting to be used to describe non-Communist Parties. This was a policy which was driven hard in the KPD as the leader, Ernst Thalmann, was an ardent Stalinist; it's around this time that not only did the KPD turn onto the SPD but it actually collaborated with the Nazis on a number of occasions.

The logic behind collaboration with the Nazis is that the KPD saw the Nazis as a fellow revolutionary working-class party which shared the same aim, the destruction of the Weimar democratic order. This led to relatively frequent collaboration in pushes for the collapse of the Reichstag as well as collaboration in physical attacks on Social Democrats on the streets. The tactic is also one that was seen as potentially having entirely selfish benefits as the KPD and the NSDAP hoped to poach eachother's working class membership. To this effect, the KPD did push a very nationalistic rhetoric in the late 20s and early 30s very much in the vein of the kind of nationalistic rhetoric Stalin would use; unfortunately it was to no avail as the KPD failed to make any significant inroads in the NSDAP membership.

As I said, someone will be able to give a more detailed answer with regard to the specfically German context but it basically went from one to the other with a pinch of collaboration with the Nazis themselves.