I found a definition on wetfeet about investment banking.
What I-Banking Is
"It is an umbrella term for a range of activities: underwriting, selling, and trading securities (stocks and bonds); providing financial advisory services, such as mergers and acquisition advice; and managing assets"
I thought managing assets belongs to investment management. Am I just confused between i-banking and the i-banking division (IBD)?
I think it is a poorly worded definition. I would say that i-banking is mostly about the process of bringing securities to the market and advising clients on various business matters, such as M&A. I think the managing assets they are talking about is in reference to advisory work with the companies in helping them manage their assets, not portfolio management from a mutual fund or hedge fund perspective.