Earlier quoted context omitted.
The rule they are talking about is the Volcker Rule. Prevents certain banks from proprietary trading. They are only allowed to buy and sell for the purpose of market making. This, of course, is an incredibly stupid rule. There’s not really a big difference between market making and proprietary trading in the first place.
Proprietary trading is trading your own money with no obligation to transact or do any business with others. Market making is offering public liquidity as part of a market function. They are designated market participants with rules and responsibilities. They are not the same.
Consider the London Whale incident — the entire $6b shortfall was a giant prop position passed off as a hedge.