This is something I've thought about a lot. Edward Boches, creative director and advertising lecturer has a nice way of looking at it.
Advertising that gets digital:
"Digital isn’t a thing. In an age when anything can be converted to a shareable file, everything is digital. All advertising needs to understand how we behave in the connected world. The creators behind these ideas (examples in link below) clearly understood [this] and they conceived their campaigns with that behavior in mind."
Advertising that is digital:
"The second kind of digital advertising are ideas that require the creative team to know and use technology beyond Twitter and Facebook. They’re ideas and executions that call for developers and creative technologists. These ideas can’t be made simply with words and pictures. They’re built using technology. Everything from sensors and apps to augmented reality."
I've butchered Boches' quotes together, so please do click the link below to read his more eloquent explanation with examples.
At impero we don’t 'do digital’, we create ideas, stories, communications & connections for this digital age. And if other agencies are involved, we work as closely as possible with them to ensure all elements of a campaign will resonate as strongly as possible with the needs and motivations of an audience that lives in this digital world of ours.