I use two vocabularies, one for tags and one which determines where a view will be displayed. Can anyone tell me how I could output the terms of my former category while hiding the ones in my latter category?
Assuming that the row style of your view is "Fields", add a "Taxonomy: All terms" field to your view. On that field's settings form, you will see a "Limit terms by vocabulary" checkbox. Select it and choose the vocabulary you want to show.
What you want is to display the terms of a vocabulary. The views module is great for this. You can create a view showing terms and select only to show the ones in the vocabulary of your choice.