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As Chris Drost mentions in his answer, the difference between the figures is caused by whether the various definitions include or exclude the bare propagator $b$ [cf. e.g. the last sentence in the first paragraph on page 3 of the second reference]. The first figure (fig. 5) states that the 1PI 2-pt fct (amputated, incl. bare contribution) $$ A~\equiv~ ...


They are subtly different. First: the first document seems to be happy to assume that something could be in the C part that is not in the 1PI; the second document seems to be trying to reduce everything that happens to the 1PI. Second: both documents seem a little sketchy about whether they include the trivial contribution (-->--). You can definitely do ...

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