In my opinion, these two triggers have different working scope.
Assuming we set one CI build as release artifact, according to my test:
1.Continuous deployment trigger:
Whenever we have a new version of the Build, it triggers the release. It means that no matter the build pipeline is triggered by manual run, CI trigger or build validation in branch policy, the release is triggered when there's one newer build.
2.Pull request trigger:
It has a smaller scope, it will be trigger by the build pipeline which is trigger by build validation in branch policy.
(Which is triggered by PR, so if we create new PR=>It triggers PR build=>It triggers PR release)
Feel free to correct me if I misunderstand anything.
Update1:
Here's one pic about my two tests:
Release-8 is triggered by my manual running Build pipeline with only CD triggered enabled. And Release-7 is triggered by PR build with only PR triggered enabled. (I only enable the Pull Request for deployment in Stage 1)
Apart from working scope, these two triggers also have a little difference here. The Pull Request Deployment in stage for now is only for PR trigger in Artifact.