I am trying to pay my PA state estimated tax, but there is a required box for “declaration amount” that is separate from the “payment amount” box. What does this mean?

From the PA instructions:

Enter the amount calculated on Line 36 of the REV-414 (I), Individuals Worksheet, in the Declaration of estimated Tax block, which is a required entry;
Enter the amount you are remitting in the Amount of Your Payment area. The Amount of Your Payment is usually determined by taking the Declaration of Estimated Tax block divided by 4.

The Declaration Amount, line 36 of REV-414(I) is your calculated estimated tax for the entire year.  The Payment Amount is the amount you are remitting with this particular payment.

Simply put, the declaration amount is what you believe your taxes to be and the payment amount is just that, what you are going to actually pay off that amount.  Unless you don't have the total normally these amounts will be the same.