I have stumbled upon some literature on Deligne-Mumford stacks, and it seems to me, at least superficially, that there is a strong link between DM-stacks which have "trivial generic stabilizers" and "effective etale stacks" in the sense of:

Intrinsic Characterization of when an orbifold (or more general stack) is effective?

However, the references I have found do not define what it means to have trivial generic stabilizers, but rather assume the reader is familiar with the terminology. Would someone mind telling me the precise definition?

Also, is there much currently known (or in the literature) about the precise link between DM-stacks with this properties, and effective etale stacks?

anyetale atlas from a scheme. But isn't it more "geometric" to say that the given stack contains a dense open substack that is an algebraic space? – user76758 Nov 28 '13 at 4:02