Perjury and false statements are both felonies, punishable under federal law by up to five years in prison. While the two crimes have similar elements, there are some important distinctions. Here is an explanation:
The crime of false statement involves knowingly and willfully making a false statement to a government official (such as an investigator) about a material fact, or falsifying or covering up a material fact. This latter point includes knowingly omitting information that is material. The key point is the speaker's intent: that the speaker has knowingly made the false statement, or omitted relevant information.
A material fact is information of fundamental importance to a case, not information either peripheral or irrelevant to the issue being investigated.
A person commits perjury when he intentionally lies under oath, usually while testifying in court, administrative hearings, depositions, or in answers to interrogatories. Perjury can also be committed by knowingly signing or acknowledging a written legal document (such as affidavit, declaration under penalty of perjury, deed, license application, tax return) that contains false information.
Perjury can be difficult to prove. The testimony of one witness is not enough to support evidence that the testimony was false. There must be additional evidence, from either the testimony of another person or other evidence.
A person can be charged with both crimes if the same lie is repeated -- once under oath before a grand jury and again to investigators during the course of an investigation. Prosecutors normally choose to charge someone under one or the other.