could you explain some key differences in the functioning/qualities of someone who's a mage of blood vs. seer of blood please?

Thing is… There’s really not that much of a difference? In practice, with specific examples, it could be much more specific. In theory? They potentially have the exact same set of powers. It’s just how they use it- To benefit themselves or others- And the POSSIBLE leanings they may have, directly using them to do something themeslves vs guiding others through their knowledge, or coming to a conclusion themselves through introspection vs coming to learn something, for example. Even the ‘Mages do the Miracle part of Prophets, Seers do the Knowing part of Prophets’ thing is reductive, since Seers can very much gain power and use their knowledge and Aspect for miracles, and Mages can easily just guide others with their knowledge, so it really is a case by case basis and a more general Active/Passive leaning rather than any big difference between the two Classes.

And the same applies somewhat to every other Class.