"How To Refer To Options?"

All options contracts comes with its unique options symbol, which is the Slv120121c40 in your question. However, unlike in stock trading where you refer to the stock you wish to trade by its symbol (MSFT for Microsoft for instance), options symbols are extremely complex with strings of numbers which can be easily misquoted through the phone back in the days before online brokers. As such, options traders developed the convention of telling the brokers the specific stock, month, strike and type directly instead of the options symbol itself, which is the "Jan 21 slv call" in your question.

However, in today's world of online brokerages, almost all options trades executed by retail options traders are performed online. If you look into your online broker interface, you will almost definitely see options quoted in the stock, month, strike and type convention as well rather than the symbols. As such, it is almost a fixed convention across the options trading world to quote options that way. In fact, if you would to express an option by its symbol to a professional options trader today, don't be surprised that options trader don't know which contract you are talking about. Basically, nobody quite pay a lot of attention to the specific options symbols anymore.

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