A 10-k is an annual filing required by the SEC for companies over a certain size, which provides the regulators with more detail than can be found in an Annual Report.
If a company has over $10 Million in assets and equity shares divided among 500 or more people, it must file a 10-K within 60 days of the end of the fiscal year, as well as 10-Q filings quarterly, whether it is publicly or privately traded. The 10-K will include specific details that companies may not have put in their Annual Report to shareholders, such as executive compensation, subsidiaries, audited financial statements, lawsuits, and so on.
The Annual Report to Shareholders can be more of a marketing piece, but the 10-K contains all the technical information that an investor would need to know before purchasing equity or debt from the company. The SEC mandates that the company releases 10-k information to all shareholders who request it.