Is there a way to login to the production and sandbox account at the same time and within the same window?

I have noticed if you login to one and then open an in private browser and login to another it will work

If you have SSO enabled you can log into both and not have to worry about being logged out of either one.

Thank you.

I usually use two different browsers with PROD in one and SB in the other

You are able to login to both at the same time. Just save the url to a bookmark once logged in and use that to access instead of switching roles.