Ah, no, they're not. Not even close.
Leave it to the ignorant to single themselves out. You did good.
Where am I wrong? What I see is:
First class is in the grid as 1-3 days.
Priority mail is 1-3 days “on average”
Neither is guaranteed. You have to move up to “express mail” for the guarantee.
As I mentioned First Class is available for 13oz or less, while Priority is for 70 pounds or less.
http://pe.usps.com/text/dmm100/choosing-service.htm
Express Mail®
Letters, large or thick envelopes, tubes, and packages containing mailable items can be sent using Express Mail. This money-back guaranteed service includes tracking and insurance up to $100. Additional insurance up to $5,000 may be purchased for merchandise. Sunday and holiday delivery is available to many destinations for an additional Fee. Express Mail envelopes and boxes are available at the Post Office.
Priority Mail®
Large or thick envelopes, tubes, and packages containing mailable items can be sent using Priority Mail. This service is typically used to send documents, gifts, and merchandise. Priority Mail envelopes and boxes are available at many Post Offices and can be ordered from www.usps.com.
First-Class Mail®
Postcards, letters, large envelopes, and small packages can be sent using First-Class Mail. This service is typically used for personal and business correspondence and bills.