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?).
Thank you in advance for your help.