"The architect builds the stage."
Translation:Architectus scaenam construit.
Yes, it has to do with which person is doing the action, the noun cases change based on how a noun modifies the sentence. Architectus is nominative and is used when the 'architect' is doing the action (it is also used with forms of esse).
Architecto is ablative and is used since the preposition cum is used (cum architecto : 'with a/the architect').
This brings up a few questions:
Do all job titles agree in gender with the person who holds them, or do some job titles just have their own grammatical gender irrespective of who holds them? ("La guardia" in Italian is a good example of a job title that is grammatically feminine irrespective of who holds the position.)
Are we being taught Classical Latin as it was spoken (in which case, were any women doctors or architects back then?) or are we being taught modernized Classical Latin?
I'm no historian, but may I venture that anglice or hispanice are anachronistic and highly unlikely names for languages or culture's identified 3-9 centuries after rome fell, when respectively Angle/Saxon gothic tribes entered and ruled over indigenous; or mixed peninsular Iberian gaelic/moorish/roman descendants began identifying culture, language influence, and themselves as spanish, portuguese, basque... before the crusades culminated, just as their other romance contemporaries would have been?
While anglice is most definitely an anachronism for ancient Rome, hispanice maybe not. Hispania as a province did exist in ancient Rome (mind you it was more than just modern day Spain) so they could have used a word like hispanice when talking about languages spoken in the area (of course it wouldn't at the time be a reference to modern Spanish/Castilian).
But you should note this course isn't really focused on teaching only Classical Latin vocabulary, and words like anglice and hispanice would have definitely been used at some point in the past 1000 years.