Asset Management:

• Their clients give them discretionary trading authority over their accounts and are legally bound to act in good faith
• They cater to the wealthy and usually have a higher minimum investment threshold

Brokerage:

• Brokers require the client's permission before executing a trade 
• Brokerages are open to any investor and the companies have a legal standard to manage the fund to the best of their ability and in line with their clients' stated goals.

Asset management is the practice of increasing total wealth over time through acquiring, maintaining, and trading investments that have the potential to grow in value.

However, we must keep in mind that asset management has a double-barreled goal which increases value while mitigating risk ...