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No, docker is a container in which you can run a web server. Your Laravel application would typically run on a linux machine inside a docker container.
https://opensource.com/resources/what-docker
Valet is a set of scripts to easily fire up NGINX web server and point it at your application. The Laravel application is still using your local php install, local mail server, local redis etc etc. Docker isolates those operating system dependencies into their own virtual environment.