In another question I mentioned that the Austrofascists fought the National Socialists. Why? Did they have any important ideological differences?
tldr; Both were fascist parties fighting for power.
Austrofascism was oriented on the Italian fascists, whereas the Nazis were strongly influenced by Hitler's German Nazis. Austrofascism was derived from the conservative parties Christlichsoziale Partei and Landbund. Both more or less favoured Austrian independence from Germany, although the Landbund endorsed a union with Germany. In contrast, the Großdeutsche Volkspartei were strong proponents of a union with Germany.
In 1933, Austrian Chancellor Engelbert Dollfuss established a dictatorship, after the so-called self-elimintation of the parliament. To secure his dictatorial regime, all opposition parties were banned. The Communists on 26 May 1933 and the Austrian Nazi Party on 19 June 1933. In 1934, Nazis attempted a coup d'état, the Juli Putsch. Thus, relations between official Austria, ruled by the Austrofascist regime, and the Nazis were bound to be bad.
The Austrofascist state was initially allied with Mussolini's Italy, which was suspicious of Germany. Fascist Italy feared pan-German Nazi-Germany could annex Austria, and become the dominant power in central europe.
However, relations between Hitler and Mussolini improved, which left Austria without any allies. Thus, Germany increased pressure on Austria, until it forced the so-called Anschluss (the unification with Germany) in 1938.
Some differences in ideology:
Relations to the church The Austrofascist ideology was strongly Catholic, whereas the Nazi ideology was at best indifferent to both Christian denominations.
Nationalism The Austrofascist ideology is strongly Austrian nationalistic. The Nazis view Austria as more of history's accident, as they viewed it as a part of the German Reich. After the Anschluss, the name Austria was pretty much eradicated. Austria (Österreich) became the Eastern Marches (Ostmark).