For the silver coins (Barber's design) a normal mirror-like proof dies was used (nothing but a polished die). For Saint-Gaudens and Pratt gold, the coins were struck from new dies on a medal press. If satin proofs were wanted, the coins were delivered as-is. If sandblast (incorrectly called "matte") was wanted, the coins were individually sandblasted just like medals; this made each coin unique as far as precise texture was involved.
The minor coins - Lincoln cent and Buffalo nickel - were issued in too large a quantity to individually sandblast the coins, so new dies were sandblasted, hardened, and then used to strike proofs on a medal press.