No. Unemployment is not wages received from an employer.
Your state should have sent or will send a Form 1099-G for the unemployment received.
Enter unemployment compensation in the Search box located in the upper right of the program screen. Click on Jump to unemployment compensation
No. TurboTax separates these two entries because the income is reported to you on different forms. The income must be reported exactly as you received it. The IRS has a copy of all government forms issued and will expect it to match what was reported.
To enter Unemployment specifically, do a search for 1099-G and use the Jump to link in the search results or scroll down in the Wages & Income section to Unemployment. Click Show More and Start. Enter Form 1099-G.
See this article for more details: Where do I report a 1099-G for unemployment or paid family leave?