The one-line difference: First-Class sends a letter. Certified sends a letter you can prove arrived.
First-Class ($3.99) is right for everyday letters — thank-yous, requests, notes, inquiries. Regular letter delivery, no tracking.
Certified Mail ($9.99) adds:
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A USPS tracking number, so you can follow the letter.
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A USPS record of delivery to the recipient's address (electronic delivery confirmation — not a signature).
Pick Certified when it may matter later that the letter arrived — disputes, official notices, deadlines, or anything you might need on the record. If you need a verifiable record of when a letter was sent or delivered, Certified is the only option that provides one; no such proof is available for First-Class.
Both travel at about the same speed — Certified is about proof, not speed. You choose the mail class on the Preview & pay step, right before checkout.