v2 refers to the team version, while (second run) refers to chronological order of streaks with the same team. So GG Unit first posted a 332 win streak with Sableye / Durant / Glalie. Then he rebred Glalie, changing the gender and EVs (as described here: http://www.smogon.com/forums/threads/battle-maison-discussion-records.3492706/page-91#post-5733552), and posted a 537 win streak with v2. Then he posted a subsequent shorter 369 win streak with the v2 team, which I identified as v2 (second run). So though my identifiers may not be super clear, there is method to the madness!!
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