Daytime Running Lights (DRL) and Automatic Headlights are a bit different.

You are talking about DRL. Only front lights and often no as bright as normal Headlights.

Cars with actual automatic lights have a light sensor that will turn on all of the lights when light level below some level and in many cars will also turn on all of the lights when you active the windshield wipers.

You can usually tell from the instrument cluster. DRL does not light up the cluster but full light on will.