No. You do not enter both forms W-2 and W-2c on your tax return.
Form w-2c only lists the boxes which are corrected.
As this form W-2c is only to correct your SSN, you just enter the numbers as shown on the form W-2 and enter the correct SSN.
After you have entered your W-2 form, continue the TurboTax interview. When you get to the page Let's check for uncommon situations, put a check mark on W-2 was corrected by my employer (Form W-2c).
See attached screenshot.

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