A public company has shares of stock that represent an ownership interest and are traded openly on one or more stock exchange like NASDAQ or NYSE. Government reporting requirements make it easy to find information about them.
A private company is not traded on any stock exchange. Don't have to file documents with the U.S. Securities and Exchange Commission. Finding information on private companies can be quite challenging. See Financial Benchmarks below for one way to approximate financials.
Nonprofits are formal organizations in the United States that qualify for tax-exempt status under the Internal Revenue Code. In the U.S., non-profits usually are required to disclose information about their financials.
Industry ratios and financial benchmarks can be used to gauge the market performance of companies and forecast growth.
Often, financial benchmarks are used as a a proxy or surrogate when data is not available for a particular firm (such as a privately-held one).