Difference Between Asset management and investment Banking
This is a great question that should have a straightforward answer. Unfortunately it doesn't, because these terms are overloaded in the real world. Let's start with the most common, basic definitions:
Asset management - The management of a client's investments by a financial services company, usually an investment bank. The company will invest on behalf of its clients.
Investment banking - Investment banking is a specific division of banking related to the creation of capital for other companies, governments and other entities.
In other words, the fundamental difference between asset management and investment banking is that AM is about managing money that other people already have, and IB is about raising money that companies want but don't have.
If you'd like to avoid confusion, stop reading now. If you'd like to understand the more complicated semantics in the real world, then stay with me - the definitions change once you're dealing with the world's largest banks, the kind we call investment banks (JP Morgan, Goldman Sachs, Deutsche Bank, Morgan Stanley, etc).
Now, proper "investment banking", as we defined above, doesn't include other finance activities that go on in large banks, especially trading. The most formal definitions will separate bankers (people who raise capital) from traders (people who buy and sell securities).
In most very large banks, you'll find two major divisions called something like "investment banking" and "private wealth". Every bank will call these divisions something slightly different, but they mean the same thing.
The "investment banking division" will break down into many business functions, two of the most important being raising capital, and securities brokerage. Yes, it will include both of them, even though we just clearly defined only the first one (raising capital) as proper "investment banking". Confusing!
The "private wealth division" will also break down into many business functions, and again, two will be very important. First, there will be a group that invests rich people's money (private wealth). Second, there will be a group that invents whole new things for them to invest in. This second group is named different things at different banks, but the most common name for it is "asset management". (Also, just to maximally confuse you, some of these banks will still refer to "asset management" as the practice of managing other people's money, whether rich individuals or institutions, just like we originally defined).
But wait! Our original definition of asset management was investing on behalf of clients - how did this just change on us!? Sad but true - when a bank is so big that it's creating new ETFs, mutual funds, and other securities for people to trade in, this tends to get called asset management, and investing people's money gets called private wealth management, or for the very, very wealthy, private banking (this will include groups that do things like finance yachts, private jets, and castles).
So, more complicated definitions:
"Asset management" - creating asset backed securities or collective investment schemes (mutual funds, ETFs, etc) that are convenient for advisors, private individuals, or other smaller banks to invest in.
"Investment banking" - raising capital for other companies, or underwriting, or trading in equities/fixed income/derivatives, or selling services to hedge funds/insurance/pension firms/asset managers (prime services or prime brokerage).
So remember - an "investment bank" has two big divisions, "investment banking" and "private wealth". Inside the "investment banking" division, a lot of things happen, including stuff that isn't investment banking, and actual investment banking (raising capital). When you're talking to someone about investment banking, just keep in mind that there's at least three semantic tiers for that term - a banking institution as a whole, a business division that doesn't deal with managing rich people's money, and the actual profession of investment banking.