What does refund has been processed mean compared to being processed

It depends.

Usually it means they are just taking some extra time to process your return.

Please see the following links for additional information as well as how to track the status of your state refund.

IRS processing time and refund status

Please see the attached for more specific information as it applies to your particular state. 

How to track my refund 

@Delores60

You can find out your tax return's status in the following ways:

• You can use the IRS Where's My Refund tool.
• You can try calling the IRS at 1-800-829-1040 but the wait times may be quite long. 
• You can  view your IRS tax account.  

@iamariva1957

Did you e-file your tax return and was it accepted?
Only the IRS and your State control when and if a Federal or State tax refund is Approved and Issued.

You complete your tax return by finishing all 3 Steps in the File section. In Step 3, to e-file your tax return, you must click on the large Orange button labeled "Transmit my returns now".

After completing the File section and e-filing your tax return you will receive two emails from TurboTax. The first email when your tax return was transmitted and the second email when the tax return has either been accepted or rejected.

Note - Once a tax return has been Accepted by the IRS or a State, TurboTax receives no further information concerning the tax return or the status of any tax refund.  Only the taxpayer listed on the tax return can obtain the status of a tax refund or a tax return.

To check the status of an e-filed return, open up your desktop product or log into your TurboTax Online Account. You can find your status within the TurboTax product.

If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds

If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund