Ideally, the creative self would be the same as the regular self. The one that washes the dishes and puts gas in the car should still be the creative self, because even - and perhaps especially - in these mundane things, the creative mind should be at work. Of course, this is hardly ever the case. We tend to move through the mundane world on autopilot, and it often takes a very intentional transition to shift from that frame of mind to one of creative vision.
The goal of the creative excursion (like "inner artist," I'm also not a fan of the term "artist date" - but feel free to call them whatever you like) is to make it a regular habit to seek places, events, and experiences of inspiration. To be aware not only of what you're seeing and doing, but of how you're seeing and doing.
As mentioned before, I've been pretty haphazard about my trek through Julia Cameron's book. Because of that, I've not yet done one of these excursions. Part of the problem is that they're meant to be done alone, and I feel a little rude running off to do something fun without inviting someone along. I don't mind being by myself, but there's a certain expectation with any expedition that it be shared.
Tonight I'm going to see a play in LA. I haven't invited anyone along, so it will be me and a pen. I have very skeptical feelings about plays in general. I generally feel they're designed more for the performers than the audience. I am hoping to be converted into a theater-goer tonight. I am hoping to learn to be a little more brave in my choice of creative outings. I am hoping to enjoy the performance and discover something about Los Angeles I didn't know before.
I'll let you know how it goes.