Hello Joshua,
Just to clarify: Hauptwerk is the software, Crumhorn Labs is the company that makes it.
Hauptwerk produces organ sounds in response to MIDI note-on/off messages. It also has a built-in facility to record the audio output as an audio file. However, it is not a MIDI sequencer so if you want to record and edit your performances as MIDI then you need an additional MIDI sequencer program, such as Steinberg Cubase or Cubasis or Cakewalk Sonar.
This page in the user guide covers how you use Hauptwerk with a MIDI sequencer:
http://www.hauptwerk.com/clientuploads/documentation/CurrentUserGuide/UserGuideRedirects/QuickStart-MIDISequencer.pdf
You can also use Hauptwerk a VST instrument within Cubase or another VST host program, as covered here:
http://www.hauptwerk.com/clientuploads/documentation/CurrentUserGuide/UserGuideRedirects/QuickStart-VSTi.pdf
Best regards,
Martin.