There are several different ways displays can be associated with each other. Some of these do not apply to your situation, but your post will be here for a long time and others will find it by searching, so I am trying to discuss the entire range of possibilities.
The first, that you are not using, is to "Mirror Displays". This computes a compromise resolution that is seems both displays should be able to reach, and sets BOTH displays to refresh in perfect synchrony, down to the same refresh rate.
The second is to use "Extended Desktop". In this mode the screens are concatenated along an edge of your choosing, and the second display is an extension of the displayable area of the first display.
Normally, extended desktop does NOT supply a menubar or a dock on each display.
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A feature of Mission Control allows the use of "Spaces", which are collections of apps and windows that can be swapped into the active display with just a keyboard shortcut. Using your Mac in this way takes additional steps, and ways of thinking, to assure you have collected the desired item into each quasi-independent "Space"
When you have multiple displays as well as multiple spaces, this feature generalizes so that any 'Space' can occupy any display. This is only possible when you enable "Displays have separate spaces".
punchline: if you have a menubar on each display, you are using "displays have separate spaces", and may need to adjust your thinking to accommodate the way this works.
View open windows and spaces in Mission Control on Mac - Apple Support
