If I recall correctly, Kerry's ill-chosen words referred to a case in which he voted to move something from committee to the floor, and then voted against the version that came up for final vote, because it had been amended. What he should've said was that his votes were different because they were on, effectively, two different bills.

In the case of a vote for cloture, followed by a vote against the bill under discussion, there is no difference in the content of the bill affected by the two votes.