For me, the difference between "extracurriculars" and "community service" is that the latter implies that you're making a positive impact on your community.
But, both are very valuable. Both types of activities give you the chance to show that 1) you're more than just a GMAT score and boring resume, 2) you have passion for something, and 3) you have a track record of leadership (i.e., making things happen, rather than just sitting on a committee).
If your student gov't experience shows all of these things, then focus on this, and worry less about cramming in some half-hearted community service!
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