Yes, they really are. The German socialists fell into two camps early -- those that supported Trotskyite internationalism, and those who took a posture of German nationalism to appeal to the support of the Wehrmacht.
The latter formed the National Socialist German Workers' Party, the NSDAP.
There are some good sources online that parse out the evolution of German socialism during and after World War I, which was the cradle of both the Spartakists and the Nazis. Before they crystallized and hardened their differences, there was almost a continuum of opinion on the Left, whose fundamental ideas began to gain popularity among the German officer corps as the old order became discredited by the failure of the national enterprise in the Great War.
If you couldn't see the family resemblance any other way, just look for the self-righteous zeal for repression. It's stamped on both factions' foreheads.
You didn't see my mea culpa down the thread... I mean to write that they WERE leftists... I should post when it's waay past my bedtime. But thanks for more elucidation!