Position A edge lettering reads upside-down when the coin is placed heads up on a table. Position B edge lettering reads right-side-up when the coin is placed heads up on a table. Since the coins are struck and then go into the edge lettering machine in random orientation, if you check a large sample of dollars you will find that the split between A and B is roughly 50/50.
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I don't know of any use of APB in coins or grading. ABP is occasionally used and it stands for Average Buy Price, or what a dealer would on average give for your coin.
A proof coin has a special shiny finish on it and it is made to be sold to collectors, and not used as money.
it means that a porfecinal has authenticated and determaned the codition of a coin
PR is a grading system used for proof coins
The most expeditious way to get a coin graded is to locate a coin shop nearby - present the coin to the owner for grading. If he/she is uncomfortable to do so, he/she will refer you to a numismatist (experienced coin collector).