Do federal and state taxes get processed by different places? Is that why I got one of them first?

[mesquitebean]

Yes.   The IRS is completely separate from the 40+ state tax agencies.   Which one did you get?   How long has it been since you filed?

[xmasbaby0]

Federal and state refunds come from completely separate entities,  There is no rule as to which one will come first or how much time there will be between their arrivals.

You do not say which one you received.  If you are still waiting for your federal refund--many federal refunds have been delayed.

TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.  Many refunds are taking longer during the pandemic. 

Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 20 of your 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

[seymana]

Yes. I received my state refund. And I mailed them in around late February. We had some issues when we tried to e-file and it said to mail them in.