Separate browser windows

I don't know whether this is a Windows thing or varies by browser.

My question is, if I have open two windows (not tabs) of Firefox, or
two of Chrome, or two of any browser -- if I open, say, my bank
account or other secure Web site in one window, is it sufficient for
security to close that window after logging off, or should I close
all open windows of the browser?

Asked another way, when two windows are open in a browser, can a
malicious Web site accidentally opened in one access the usernames
and passwords I have typed in the other? If it matters, I don't let
any browser store usernames and passwords; those are all in an
external non-Cloud password manager.

--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://BrownMath.com/
http://OakRoadSystems.com/
Shikata ga nai...