An evocation element and a thaumaturgic specialization. The "method" just refers to the model of calling up power and controlling it instantly as opposed to over time. It doesn't make sense to force someone to double up on their specializations and foci for something they're supposed to already be good at.
They're good at thaumaturgy if they put all their specializations and foci in Thaum. They're good at evocation if they put all their specializations and foci in to evocation.
A wizard has to choose one or the other. (S)He can't use thaum foci for evocation.
If you have a sponsored magic, I think it should be the same. The flexibility comes in when you do things like skill replacement spells as evocation and blocks that last a whole scene.
All those things you would just do with straight up Evocation anyway.
Yes, but the subtle differences are important. If you pump all your foci in to thaumaturgy hoping to be able to do both evocation and thaum with the same foci, you still need to deal with the disadvantages that go with thaumaturgy:
- An evocation blocks are mobile but can't do a block that reflects attacks and its duration only lasts one exchange instead of sunrise. Thaum blocks are immobile and can only be set up on a threshold
- An evocation attack has a weapon value while a thaum attack doesn't have one and the accuracy of a thaum attack is equal to its total complexity
- An evocation veil is mobile but only lasts one exchange and a thaum is immobile and lasts for a whole scene.
If you want your evo-thaum to be exactly like evocation (weapon values on attacks, mobile veils etc..) I'd say that you'd need to set your foci as evocation.
When I GM, I use evocation foci for evocation and thaum foci for thaum. It's just easier for me.