I'll hop on just to add: the little plate that says "mod" can't be turned off, but for us community moderators we can toggle a little shield icon when we're trying to speak with the "mod voice." We can only do it in our communities, but (I think) the admin team is by default modded in every community and should be able to toggle that shield wherever they are.

So if you see the shield icon next to the name, that was intentionally toggled on to show they're trying to speak as a mod and not just a community member. If you only see the little "mod" nameplate you can probably assume they're just talking as a member of the community (unless context makes it obvious that they just forgot to turn on the shield).

Edit: Here's an example of how the shield icon looks to me from one of my posts; I'm on mobile with the darkly theme so it probably looks different to you unless you're also on mobile, but hopefully still a useful example: