I call myself both. I do a lot of graffiti and I consider that a form of art. but professionally I'd call myself a designer. I probably wouldn't mention that I draw and paint graff in a Job interview. But yeah it's such a hard thing to define and this automatically leads back to the question of what art is. Art can be Damien Hirst's skull with diamonds or a stuffed animal in a glassbox so why can a logo or a website not be art? And if you like childrens drawings then it can be art for you. Some people do childish styles on purpose. Oh well I'm rambling on and it's Friday so I'm gonna indulge in the art of consuming large amounts of alcohol
Have a good weekend!