@ElizaBennett - That makes sense. But sometimes the receipt is not as detailed as the invoice. Then, both for tax purposes and for your own records, you might want to save them both together.
There are two other good reasons to save receipts: warranty and insurance. A lot of manufacturers require the orignal receipt in order to honor the warranty. Even some things that you don't think of as having a warranty can be returnable if they're defective. I once got my money back for a pair of shoes that wore out unacceptably fast!
Insurance companies also like to see receipts if you are filing a claim for theft or other kind of loss. I don't know if it's necessarily required, but it's a good idea to keep the receipts for big-ticket items like TVs.