Numismatics has to do with coins.
What does numismatic collect
Do you mean "numismatic"? The study or collection of coins, tokens, and paper money and sometimes related objects.
Numismatics is the study of coins and medals. A society therefore would be a group of like minded people.
Gemology is the study of gems. -ology on the end of any word means "the study of." So, for example, theology is the study of God, biology is the study of life, etc.
Numismantics is the study or collection of currency, including coins, tokens, paper money and other related objects. This also includes the broader study of money and other payment media used to resolve debts.
The spelling gemmology is one variant of the word, secondary to gemology (the study of gems).
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The corresponding noun to the adjective numismatic(meaning relatic to money, coins or medals) is numismatics, or numismatology (meaning the the study of coins or medals). Although it ends in -s numismatics is a singular noun.*Although a coin collector may be a numismatist, there is no formal corresponding noun numismatism.)
Swiss Numismatic Society was created in 1879.
Royal Numismatic Society was created in 1836.
American Numismatic Association was created in 1891.
If I understand your question you mean geology.