Contact = chance for solid contact. I.e. good hits like line drives, fly balls with good trajectory/carry, grounders with some velocity on them. It's the batting average rating - or, more precisely, the rating that helps govern BABIP.
Vision = chance for the hitter to make contact at all on the pitch. This influences the hitter's contact % when he swings, but has no bearing on quality of contact.
The PCI size is influenced by both, yes, though the results tend to weight one heavier than the other.
A hitter with high contact and low vision will hit the ball hard when he hits it and should carry a good BABIP/productive hits, but is prone to the strike out, especially if he's fooled by the pitch (i.e. your timing/swing plane isn't good enough). Chris Davis for me is an example of this. He has 80 Contact but 40's PVis. Many of his outs are via the strikeout. In my franchise's last season, he hit .306 with a .318 BABIP and struck out 139 times in 577 AB. 34% of the outs he made were via the K and he led the team in K's (and I play every game - so that's all user controlled)
A hitter with low contact and high vision should make contact a lot, but the quality of that contact is likely inconsistent. Instead of a K, he might hit a 4-hopper to the shortstop or an infield fly ball. On the other hand, if contact is needed, like on a hit-and-run or where that 4-hopper scores a guy from 3rd, a high vision batter is the man for the job. Same for sac flies. He might hit a lazy can of corn to the center fielder, but that might be all you're asking for, too. An example of this from my team is fictional Jose Campos (a MLB14 draftee). He struck out just 45 times, but batted only .237.
A hitter with low contact and low vision is a tough guy to deal with. He will probably be very inconsistent as he's not likely to make a lot of contact and the contact he does make might not be good. I picture these guys susceptible to "hot" and "cold" streaks - or a guy that's good as long as things are going his way (hot), but if he falls into a rut, forget about it (cold). I have a guy with 48 Contact and 45 vision and above average power...and he's batting .198 after a solid rookie year (.270).
A hitter with high contact and high vision is a nasty guy to face. You won't get him to K much and when he hits it, it's like a tough ball to defend. These are your consistent high average types unless they get bad luck or are in a deep slump. Heaven help you if he has decent (or better) power as well.
What you mention about chasing pitches is the DISC rating for the CPU. Vision impacts how they place their PCI as well as the size of it. PVis is "countered" by the pitcher's K/9 rating, which is modified by the individual pitch's movement rating.
Basically:
Disc = OSwing % (out of zone swing percentage) - not sure if any pitcher rating "counters" this, perhaps pitch movement?
PVis = Contact % (both in and out of the zone) - "countered" by K/9
Contact = BABIP/solid hit % - "countered" by H/9