Different keyboard mapping on external keyboard

Solution 1:

The mapping of the input source you have selected in the "flag" menu should always apply to both the internal and external keyboards. The standard US keyboard has one less key, so it will be slightly different:

If yours does not behave that way, something is wrong.

Solution 2:

At this time, macOS does not support having different layouts on internal and external keyboards. Source: Me. I've dug around on the System Preferences in macOS Big Sur (11.1).

However, you may find value in Autokbisw, an "automatic keyboard input source switcher". Source: I heard about Autokbisw from https://superuser.com/a/1150616.