What is the difference on the IRS website between IRS acceptance and IRS approved?

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

I don't think the IRS says Accepted.  They Approve your return and refund.  Accepted only mean the IRS accepted your return for processing.  Then they approve it and send the refund.  

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

 

 

You need your filing status, your Social Security number and the exact amount  (line 35a of your 2023 Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund