In a CDS (Current Environment), you have to option to Run the Flow under a context of a certain user. And there are a few options from which you can select from – Process Owner, Record Owner & Triggering User

Here’s my Flow in which the trigger is the CDS (Current Environment) connector. Show advanced options and you’ll see that there’s a field call as Run As


Which has the following 3 Options as I mentioned above –

Let’s look at each one of these.

Scenario

To demonstrate Run As, my Flow is triggering on the Update of the Account record, an attribute in the CDS (Current Environment) connector called as RunAsSystemUserId provides the GUID of the System User used in the connector’s Run As field.

You can use triggerOutputs() function to get this GUID from the Trigger Outputs and use it to fetch the System User record. To see how triggerOutputs/triggerBody() works, check this post – Using triggerBody() / triggerOutput() to read CDS trigger metadata attributes in a Flow | Power Automate

Process Owner

As suggested, Flow Owner meaning the one who Owns the Flow

1. If I select as Process Owner, no matter who triggers the Flow or who is the Owner of the record, the Run As user will be the one who Owns the Flow.
   
   
   The record could belong to one owner and the other owner might modify it as shown below –
   
   
   
   But the Flow will Run As the Owner of the Flow as suggested.
   
   
   
   
   Multiple Owners?
   In my test, I believe the one who created the Flow becomes the first Owner and hence, is what it appears in Run As
   
   

Record Owner

1. Easily, the record Owner in Dynamics 365 is the Owner of the record, so no matter who triggered the Flow or who the Flow owner is, the Record Owner will be the Run As user.
   
   
2. In this example, Priyesh Wagh is modifying the record Owner by Kuldeep Gupta, the Flow Run As will show as Kuldeep Gupta
   
   

Triggering User [Also Default]

1. If the Run As is set to Triggering User, whoever caused the Flow to Run is the Run As context user.
   
   
   Let’s say Kuldeep Gupta is a user is modifying a record Owned by SYSTEM, the Run As user is Kuldeep Gupta.
   
   
   
   
   
2. Now, if there’s no Run As selected or even if there are multiple Owners to the same Flow, the one who causes the Flow to run, is the context user of the Flow.
   
   
   Let’s say Priyesh Wagh modified this record owned by SYSTEM, the Flow will Run As Priyesh Wagh
   
   
   

Hope this helps!!

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Thank you!!