TurboTax automatically put in amount of $569 for our prior year state refund but that is way different from the amount we got as a state refund, so why the difference?

Yes, there are a number of reasons why the state refund shown isn't what you actually received:

• If you amended your state return after it was filed, the amount shown may be the original refund, not the corrected refund.
• If your state refunded additional money to you such as the NY STAR credit, the Colorado TABOR refund and many other state programs, the additional tax refund may not have been included in the total. 

Regardless of why there's a difference, it's important to make sure the correct figure is reported. To correct the state refund that you received:

1. Open your TurboTax account.
2. Select the down arrow to the right of Income & Expenses.
3. Select Review/ Edit.
4. Select Start or Revisit to the right of Refunds Received for State/Local Tax Returns.
5. Answer the first question Yes.
6. Edit the details about your refund, or the information from 1099-G here.

....and...which one was higher.

IF the Software's number was higher, it could have been true for other reasons too.

Checkoff donations to charities that came out of state refund?   The refund before the checkoff is used.

OR, maybe you let the state keep some of the refund against your eventual 2023 state taxes.