Given that some older proofs may not be recognized as a proof, what happens if you submit a 19th century coin as a MS on the form and it's actually a proof? Will they catch it and grade it as a proof? Are there tell tale signs on dimes that indicate whether they're a proof or not? Sometimes they may have circulated and may be toned and more difficult to tell. Could a grader overlook it and grade it MS or is that not likely?
It is sad when two genuine coins that you can't tell apart have much different values. Is that the road down which US-coin collectors have chosen to go? Collect ancient coins and you won't have to spend so much time worrying about such considerations. Instead, you can think about its history and whether you like the coin! Here is a link to the CT ancients forum: https://www.cointalk.com/forums/ancients/ Take a look around and see how much they enjoy their coins and how little they worry about grade (They worry some, but not as much as US-coin collectors.)
In most cases, NGC will attribute the coin properly (if you mark "MS" on the form and it is "PF" then they will grade it as a PF XX). They could make an error too but for the most part they get it correct. As far as attribution for your coins, start a thread here and someone will likely be able to help (as we do have people that specialize in these early proofs).
If all the US Coin collectors start to collect ancients, that would be really good for the market value of your collection.
They is more than one way to determine if a circulated coin is a proof. Different dies are used, for one. Also, the rims on proofs are more squared off than on circulation strikes.
Generally, different dies are used, but not always. There are many instances of both business strikes and proofs sharing the same dies.