Self-funded and bootstrap funding makes sense if you are already rich, or the product or service you intend to sell is ready for the market and you don't need to look for outside funding. It's tough to make bootstrapping work, though, because there are lots of marketing and sales expenses even after a product is developed. Even one-person consulting companies or small service companies (like accounting or bookkeeping firms) will usually find a period where they don't pay themselves because the money doesn't come in evenly over time.
Seed capital and angel investors are people willing to invest a small portion of their wealth in very early stage companies, usually where there is only a concept of a product or a very rough prototype. You might have to convince just one person to make the investment, so the decision can be quick.
Venture capitalists (VCs) are small to medium-sized partnerships devoted to assessing, valuing, and investing in companies. They pool money from wealthy individuals and institutions (like pension funds and colleges) and spread that money over a portfolio of companies. They are focused on their 'exit strategy' - how they will get their money back (and more) - usually by taking a portfolio company public in an initial public offering (IPO) or by having it acquired by an existing, richer company. Because their real clients are the Wall St firms that will take the companies public, the VCs tend to act like 14-year old girls when it comes to following fads. If investors are clamoring for social networking or green companies, the VCs will happily oblige, whether or not the world needs another one.
Private equity refers to closely-held partnerships who typically provide financing for special occurrences like buying a bankrupt company, splitting a company into component parts, or taking a company private.
Partners can form partnerships, where each person contributes capital to the organization from their own personal assets or by guaranteeing a loan from a bank or third party. If the partnership runs out of money it can issue a 'capital call' to the partners to get them to pony up more.
Lenders loan companies money and they expect to get paid back with interest over a period of time (which can range from days to 30 years). The loan can be secured by assets of the company. The loans are called 'bonds' and can be bought and sold like stocks.
Investors in public companies buy and sell stock on public stock exchanges, like NASDAQ. The only time the company receives money is during an initial public offering (IPO) or secondary or subsequent offering, or when company-owned stock is sold. The rest of the time investors are trading between themselves.
The government also has a variety of loans and grants for small businesses, especially in areas of defense technologies.