"Accepted" is that the IRS e-file system's basic checks (SSN,name match, date of birth, all required fields are filled in, and other basic security checks pass so the IRS will accept the return into the processing system (no actual processing happens in the e-file checks).
"Approved" means that the return has been fully processed and the system has not found any reason to deny the data and/or refund.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**