# Direct union of finitely generated subgroup

I'm reading Wagon's book "The Banach-Tarski paradox". At page $$149$$, the author talks about the "direct union of a directed system of amenabile groups" without defining it.

Q1: does direct union simply mean union? If this is the case, why does he use the adjective "direct"? Or is direct union the same as direct limit?

Q2: the same author states that "any group is the direct union of its finitely generated subgroups". It seems clear to me that finitely generated subgroups form a direct system (right?) and it seems almost trivial that the union of all finitely generated is a subgroup that, actually, equals the group itself (right?).

1. For Q1 this means "direct limit." I suspect that in his setting, each homomorphism $$f_{ij}: G_i\to G_j$$ in the directed system is injective, so it makes sense to identify groups $$G_i$$ with subgroups of one large group $$G$$ such that each $$f_{ij}$$ is the inclusion map $$G_i< G_j$$ and $$G$$ is the union of the subgroups $$G_i$$.
To say that some $$X$$ is the direct union of a collection of some $$Y_i$$'s means that $$X$$ is the union of the $$Y_i$$'s and that the $$Y_i$$'s form a directed family (any two of them are included in one of them).