IB vs PE vs HF vs CO vs TR vs AM vs ER vs CF vs VC

You could broadly categorize these fields you listed into three categories: buyside, sellside, and industry. 

Industry is pretty much companies in general, and a role in CF (corporate finance) falls into this category. On WSO, this category caters towards roles such as Corporate Development and Corporate Strategy. In general, you'd get into these roles after a stint in banking or consulting. 

Then you have the buyside, which invests in companies. Now, this could be in the form of AM (asset management), which is usually investing other peoples' money into stocks, bonds, etc. The most stereotypical AM firms are places like Blackrock and Vanguard (the guys who run the most popular ETFs). Then you have hedge funds (HF), which are, in the most simplified terms, spicier AM firms. Hedge funds cater to wealthy investors, can make use of options and short selling, and generally allow for some pretty creative plays. Despite hedge funds theoretically being stable (hedged and uncorrelated stream of returns), in practice they tend to be pretty risky places to build careers relative to some of the other careers out here. Oh, and hedge funds usually invest in public markets.

Private equity (PE) firms invest in private companies that aren't listed on any exchanges. They'll usually buyout entire companies and take on debt to do so. PE is one of the careers people in this forum love to idealize, with the large pay being a major reason. VC is venture capital ,which are firms that purchase equity in startups and early stage companies in some of the "sexier" industries like healthcare and tech.

Then you got the sellside, which provides services to the buyside and companies. IB is investment banking, which usually does financing work and advisory work. On the financing side, they'll help companies raise money through debt and equity, so these are the guys usually leading IPOs. On the advisory side, they'll help companies buy one another (M&A), restructure their debt, come up with defence strategies against hostile takeovers, etc. Equity Research (ER) guys publish reports on companies, which are then sold to investors. Traders (TR) help provide liquidity in a variety of asset classes, like stocks, bonds, commodities, structured products, etc. Consulting (CO) is a very wide title, but on WSO most people are talking about strategy consulting at the top firms, where consultants research strategy plans for corporate clients. These strategies could revolve around expanding into new markets, introducing new product lines, etc. 

Out of undergrad, you're generally going to start in something like banking, consulting, trading, or equity research. Consulting opens many doors for you such as Corporate Strategy, Private Equity, and Venture Capital. Equity Research is a pretty known way of getting into hedge funds, as is trading. Banking can get you into pretty much all these categories, because it is the broadest career with so much variety in the kind of work you do.

You'd generally start out in banking as an analyst. 

I know my answer is pretty general, so if you've got any specific questions, the more experienced people on this forum would be better suited to answer them.