Engineer - Always produce the physical, practical know how, calculations and mechanical drawings or models or building blocks in order to produce something. - Sometimes generate the ideas for the product user-interaction and for production.
Designer - Sometimes produce the physical, practical know how, calculations and mechanical drawings or models or building blocks in order to produce something. -Always generate the ideas for the product user-interaction and for production.
Artist - Produce something which interacts with the senses of the audience. Something which conveys feeling or meaning which the viewer / user can interact with, - identify with or react against or feel in some other way.
I think that a designed product should have some of all of these three. Not sure if it's THE definition of a designed product but it's my definition.