To be proofs, they muat be struck at least twice on a medal press, not a coin press - higher pressure and slowly. Not all SMS - especially 1965s (or proof coins for that matter) are mirrored. There are satin proofs, like some of the 1936 issues, and some of the pieces from the early 1950s, which are my favorite.
It's pretty complex and the '65 is far more complex than the '66 and '67. The mint used many different processes to make the '65 SMS and if that weren't complex enough they used retired SMS dies to strike coins in San Francisco without a mintmark for circulation. Essentially just about everyone can be correct. But I believe that the SMS coins (and later mint set coins) were struck with more pressure than the proofs but almost all were struck only once. I believe a tiny minority were inadvertently struck twice. Those I've seen struck twice (technically these are proofs) had no trace of frost at all. People would be surprised with some of the stuff that shows up in SMS sets and in circulation as well. There are ugly low relief 1965 quarters that are so shiny they look polished and are usually mark free. Strange things appear in these sets.
I do not know for sure, but it seems that I read a long time ago, that there is no way to tell the difference between a business strike or a SMS coin. The only way to know for sure, is if the SMS coin was still sealed in the original plastic that it was issued in. Once removed from the original plastic, and the SMS is mixed with regular business strikes, there is no way to tell the difference. That was my understanding anyways.
That may be true in some cases, but I've bought a few and from what I can see it's very easy to see the difference.
I wager if you mixed 500 nice '65 quarters with 500 SMS's I could usually separate them with 100% accuracy. It gets way tougher if you mix Gem BU with SMS but the accuracy would still be pretty high. I'd get more SMS in the Gem pile than Gems in the SMS pile. '66 and '67 sets are not "sealed". You can open and close them easily. If more people saved more '65 quarters it would be harder to separate them. There just aren't many Gems and the true oddballs like Gem coins made from retired SMS dies are scarce or non-existent. It's the oddballs that can be hard to classify, the others are just experience.
I might add that the services err toward calling high grade coins "SMS'. Some of these probably are actually GemBU but they don't want a bunch of SMS posing as Gems.