Yes, the PUA or UC preceding the 1099-G form name is used to report different types of unemployment benefits received but do not change the way it is reported on your tax return.  It is for reporting unemployment compensation received.

When you file your federal income taxes this amount must be reported on your Tax Form 1040 or 1040A.

If you received UC-1099G and PUA-1099G forms the amounts will have to added together before reporting on your tax forms.

If the box numbers don't match then go by the description for each box when inputting in TurboTax.

Here is a link with additional information:

Different types of Form 1099-G for Unemployment Benefits

I received PUA-1099G form and on turbotax there is no tax withheld box. How do I account for tax that was withheld on my 1099G? 

In the 1099-G entry section, please make sure that you've checked the box just below "State or Locality" entry fields that says "Federal or state income tax was withheld on this payment". Otherwise, you will not be prompted to the next screen that asks how much was withheld. I hope it is as simple a fix as this!

I have the same question and cannot find an answer.  The answer offered here is not helpful.  TurboTax asks for state and federal tax withheld separately, but the PUA-1099G only has one box that says "Tax Withheld."  It's doesn't specify federal or state.  

The tax withheld is federal tax according to Payment UC-1099G FAQS - Unemployment Compensation.