Yes, federal and state are two separate entities. If you are getting refund from both, you'll be issued two refunds.
If your federal return is accepted by
the IRS, use the federal tax refund website to check the refund status - https://www.irs.gov/refunds
If your state return is accepted, 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
Some tax returns take longer to
process than others for many reasons, including when a return:
- Includes
errors
- Is
incomplete
- Is
affected by identity theft or fraud
- Includes a
claim filed for an Earned Income Tax Credit or an Additional Child Tax
Credit. See Q&A below.
- Includes
a Form 8379,
Injured Spouse Allocation, which could take up
to 14 weeks to process
- Needs
further review in general
You can read more here - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions