When you ask Finder to copy files to a different drive, like an external drive, the default way of operating is to COPY. That is, the file is replicated on the Destination drive, and left UNCHANGED on the Source drive.
You copied them to an external drive. That is good, but you did not eliminate any files form the Source drive where you had too many.
Now you need to go back and delete those files from the 'too full' drive.
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One way I like to do that is to use two Finder Windows at once.
Open a Finder Window to show the Source folder, and move that Window to the Left side of the screen.
Finder > File > New Finder window ...
... and move that window to the Right side of the screen and navigate to the Destination drive.
Now you can compare the files in each window, and be sure you have an accurate-sized copy on the destination, before deleting it from the Source.