Last year, starting pitchers pitched 65.7% of innings and recorded 62.5% of strikeouts. The reason they got proportionately fewer strikeouts is that there are a lot of relievers who come in for one inning throwing as hard as they can. But overall, starters pitch the most innings and get the most strikeouts.
With one glaring exception: The Minnesota Twins. The Twins relievers got more strikeouts than Twins starters. (I heard this on a Fangraphs podcast.) That's partly because Twins starters pitched only 60.1% of the team's innings, the fewest in the majors. Still, a normal spread between starters and relievers would result in Twins starters getting 56.9% of the team's strikeouts. Instead, they got only 48.4%. The second-lowest was Colorado, with 55.5%. I don't know whether there's ever been a team before whose bullpen got more strikeouts than its starters. I kind of doubt it.
Twins relievers weren't exactly flamethrowers, as their 7.9 strikeouts per nine innings ranked 23rd in the majors. But the Twins starters got only 4.9, more than a strikeout per nine innings worse than the second-worst team, again the Rockies. Twins starters had the lowest strikeout rate of any team since the 2006 Royals.
The Twins have stressed a "pitch to contact" pitching philosophy in recent years. They've certainly delivered on the low strikeout part. But given the team's worst-in-the-majors-by-far 5.26 starters' ERA, they've either got the wrong approach or the wrong personnel (probably some of both). It makes for an easy comparison for incoming starters Ricky Nolasco and Phil Hughes, though.