I wanted to ask these questions too because what I understand as institution in trading is different from the definition the OP gave. Institution that I know in trading are like the market makers who have huge capital that they move the market when they execute their trades. They are also regarded as Smart Money and there are several technical analysis strategies that claim to be trading inline with them. The aspect of teaching others our trading strategy does not make trading institutionalized rather it could just be a way of sustaining the family legacy if trading is the major occupation of the family.
People who are fucking rich won't even dare to say that I only rely on trading for my income because they know it will be a lie and what we see are minions who just pretends to be rich just only to make money from others. Whereas brokers are licensed who don't really approach the customers, but the users will approach them to manage their savings and take a cut as well as commissions for each trade and in overall profits.