Quick Deploy and Fast Deploy supportQuick Deploy.
When performing a Quick Deploy the test classes in the destination org don't run because they were executed as part of a previous deployment. In order to perform a quick deploy, you need to validate the deployment previously, running the test classes, in order to get the validation key that will allow the second deployment to be performed without running the test classes.
Copado will always try to use Quick Deploy when available. If the validation key is not available or not valid Copado will fall back to the regular deployment option. In order generate a validation key, the deployment must run first as validation only deployment (CheckOnly enabled). Once this deployment is completed successful, you can disable the CheckOnly checkbox in the deployment step of the deployment record and run the same deployment record again.
The deployment will contain the validation key that will allow the deployment to run without execute the test classes again in the destination org.
Copado also supports fast deploy. This will be performed when "Run Specified Tests" is selected for the deployment. In this case, only the apex test classes included in the deployment will be executed in the destination org.
You will find more information about the Test Level deploy Options here.