GatewayRedbirds.com

Lynn's official service time, for the purposes of things like arbitration/free agency eligibility (i.e. the figure listed on B-R), includes everything from his initial call up on June 2 through the end of the season (Sept 28), which is 119 days. The main difference between the two figures is that, unlike the rookie status figure, service time for contract rights purposes includes:

-time spend on the Major League DL (like greenback pointed out, which was most of August and all of September for Lynn)
-time on the active roster in September (which overlaps Lynn's time on the DL, but in general it's a major difference between the two)
-time spent on optional assignments if it is less than 20 days total for the season (which would mean Lynn's time on optional assignment from June 10-21 counts as service time, since it was the only time he was optioned and it was less than 20 days)