One is a leaf you drink, the other is a leaf you eat
This is the difference everything else follows from. Mate is an infusion — hot water pulls compounds out of the leaf and the leaf is thrown away, so you get whatever dissolved. Matcha is a suspension — the leaf is ground fine enough to stay in the water, and you swallow it. That is why matcha delivers more of the leaf's catechins and all of its fibre, and it is also why matcha costs more: only shade-grown leaf with the stems and veins removed is worth grinding, and grinding it on a stone mill is slow.

