The arms of the Defense Force were the infantry, cavalry, artillery, and a tiny engineer corps.
Infantry can be divided as I wrote above. The regulars of the Habsburg empire, the Hungarians were serving outside of the country, these units had to return home. Then there was the newly set up Home Defense Forces, and the national guard it grew out of. I think border guards also count here. Beyond were the volunteer militias, the "Freikorps". As auxiliaries forigners also fought alongside of our boys, first and foremost the various legions: the Viennese students, the Polish legion, and a German one, with skull and bones on their cap (srsly). Italians arrived too. (Curiously Vlahs did negoitiations with the Hungarian government for an own legion, even offered that the whole Avraham Iancu revolt side with us, and turn Wallachia and Moldova against the Russian. Srsly.)
Cavalry always remained hussar centric. It was the classic Hungarian role, the Emperor and King had no curiassiers from this part of his lands. There was a weak little step to set up such branch, but resulted in only one regiment. Other light cavalry units could be found too, eg. uhlans and chevau-légers.
As for the artillery corps, this stood on the most wobbly legs. They took the Austrian model as a template as the organized this branch of the military, which had a quite complicated structure since it also included logistical organs. This branch also included the artillery of garrisons and forts. Problem were that the troops of the arty units stationed on the Hungary were almost exclusively Austrian and Czech, on the other hand quite a few were willing to help setting up armament factories, if not involved in the struggle directly - sometimes as PoWs. Which was a great help since the inherited cannon park lacked the pipes that could be fielded in battles.
Despite the arty corps origin there were differences compared to the imperial. First a battery consisted only 8 cannons, this was lighter than the Austrian 10 (although I think they had light and heavy batteries too). So less firepower on paper. However the horse train Hungarians moved the pipes around were more maneuverable, which offered tactical advantage.
The engineers were sappers and pontooner battalions.