someone can correct me if i'm wrong...
yes, both have practical components to it. Iirc, Theatre is more "technical" and Drama more like you can sort of pick yourself.
Basically what I mean is that Theatre Studies involves you taking off monologues and scripts from the syllabus whereas in Drama you can write it yourself.
Theatre Studies also focuses more on stagecraft whereas Drama is more about non-naturalistic performance techniques (actually Drama does have questions about stagecraft too).
Theatre Studies also involves a folio.
With the solo performance exam, Theatre Studies involves performing off a script (from the syllabus) but you apply stagecraft techniques (acting + direction OR design)
Whereas with Drama, you write your own script (based on a topic choice from the syllabus, changes each year)
Both also involve watching a professional performance and you have to answer questions about it. Obviously they're not about narrative/plot but rather technique
so yeah, both also have written components too.
hope this helps