i am probably not getting the subtleties of your question, but here goes.
my understanding of solidarity is that it is much like mutual aid. that the point of it is that it is reciprocal.
charity is one way, and implies (at least to me) a martyrdom on the part of the giver, as well as a desire that the recipient live up to the charity, or change in some way.
but that doesn't distinguish solidarity from mutual aid much, so maybe someone has a better answer.
and as with many things, solidarity seems to be getting to be a word that people use in an empty way, to express broad (and meaningless?) support.