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In analogy to QED, the following Feynman diagram is a diagram contributing to the vacuum polarization effect, leading to anti-screening, asymptotic freedom and running of the strong coupling constant. It can also be interpreted as a correction to the propagator of the gluon.

(Of course, there's no true analogy to this diagram in QED because photons do not couple to themselves, and here we make use of the existence of a 3-gluon vertex. In QED we would have a fermion-antifermion pair instead of bosons in the loop, similar to a gluon going to fermion-antifermion and back in QCD.)

My question now is about the following diagram which has a 4-gluon vertex:

Does this also contribute to vacuum polarization and the effects it entails? Or is it something conceptually different? (It seems different because we don't have the splitting of one object into two and back.)

(PS: Feel free to add more meaningful tags and correct any statements in the above which are wrong.)

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Yes, this is another diagram that contributes to "vacuum polarization", also called self-energy. If you want to make a consistent calculation of the self-energy in perturbation theory, you need to include the two diagrams that you mention, plus the diagram where the gluon splits into $\bar{q}q$, plus, depending on your gauge choice any ghost diagrams.

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Even though technically you must take it into account, it turns out that in four spacetime dimensions its contribution is zero. For more details see P&S page 524. – PPR Jul 21 '14 at 22:12

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