What Is The Difference Between Investment Banking And Asset Management???

An investment banker arranges for financing a business by selling its stock to the public, arranging a merger, or taking a business public.

An asset manager provides the service of managing the assets of a person or another entity. This may involve managing stock and bond portfolios, or managing real estate assets.

The same company may act as investment banker and asset manager, but they are separate functions.

Think sell-side vs buy-side. Asset managers manage investments, selecting stocks, bonds, or other investments that will appreciate in value for their investors. They're on the "buy-side."
Asset managers are anything from hedge funds to index funds, insurance companies, pension funds, mutual funds, and a few investment advisors. The largest asset managers are pension plan funds and insurance companies.

Investment banking can be a number of things but it usually refers to activities that raise capital for firms, in the form of either debt (bonds) or equity (stocks).
The debt markets are probably a hundred times larger than the stock exchanges (bonds are generally "safer" investments than stocks).

New issues (IPO's), seasoned equity, bond issuance, mergers, acquisitions, and divestitures (sales of a business or business unit), and some "securitizations" are all under the heading of investment banking.
They're called "sell-side" because after they create the new stocks or bonds, investors (buy-side, asset managers, etc) buy them to fund the business venture, in the hopes of getting a return on their investment.
The two functions are basically "buyer and seller."
A bank may do both functions, but they frequently do not, and they're separate and distinct from one another, much as an insurance company is separate and distinct from a commercial bank that takes deposits and lends money.