I've noticed some people using "spiritual" to describe notions they consider aesthetically sublime and morally uplifting but not well understood, when they are not particularly motivated to understand them, without any commitment to their being supernatural. This may be what you refer to in your second meaning, I'm not sure.

There is, of course, a lot of potential overlap here with supernatural notions.

So, a person who doesn't believe in god, but still thinks that he has an "immortal soul" or something? Thanks for explaining!

I guess, this is similar to the second part of thomblake's comment. Thank you for explaining this!

But, if it really can mean such different things, then that particular in the survey question wasn't formulated very carefully.

My impression was that something like that was intended. However, this seems to be a conflation of different categories. The normal category that occurs in this sort of context is "not religious but spiritual" which seems to generally mean people sort of like what you describe but also who ascribe to various supernatural entities (e.g. god, ghosts, spirits, maybe faeries). When given the choice between "atheist" and something like "no religion" or "none" such people will generally not put down atheist. And such people look demographically very different from atheists and agnostics. See e.g. this Pew study. My impression is that the religion questions were not phrased in a way that showed much familiarity with the underlying demographics or how such questions are generally phrased. In this particular context that's ok because I suspect that there are a fair number of people here who are atheist-but-spiritual under your definition but very few people here who would fall into the "not religious but spiritual" notion that is a subset of the nones in the general population.