"Identifying with" something or "Identifying As" something has an explicit meaning to me, which is that it is something I would call myself. Some of this may come from training and industry I'm in, but it's what you think of yourself as.

For instance, someone who doodles occasionally may or may not identify "as an artist", but anyone who paints professionally almost certainly identifies as an artist. Someone who paints regularly as a hobby probably identifies as an artist; the doodler may be more idle about it and not really think of it as being an essential quality of self: It is something that person does, not something that person is.

From such lines of thinking come statements such as, "Ich bin ein Berliner." -- http://en.wikipedia.org/wiki/Ich_bin_ein_Berliner