"C" rating has to do with internal resistance of the battery and other factors and is a somewhat non-standard "quantity"
It (supposedly) means you can "continuously" disharge at X * capacity
But "continuous" can mean for up to 1 minute or for the whole pack's charge or just about anything the person who slapped the label on wants it to mean...
There's an infamous battery maker's claim of 150C (drain the pack flat in 24 seconds) where the pack had wires which would melt at that current in under 5 seconds.
C rating meanings are pretty consistent within any given brand and as long as you are comparing within one brand they are useful.
Don't try to equate the 20C of Sky LiPo vs Turnigy vs Thunder Power vs Polyquest vs Max Amps packs. If they have any relationship its accidental.
20C will have higher internal resistance than 30C and will get hotter under the same load. You'll also waste a little more of the pack energy creating that heat.
Within the same brand packs you can expect higher C to give SLIGHTLY better peak performance at the cost of a bit of duration (due to higher current flow). Unless you are demanding high current you may not be able to notice it.
You can't even really compare the capacity of different brands well... what one labels 2000 ma another might label 1800 or 2200. I have a 3S 2200 ma 20C "Dynam" labeled pack that gives less duration than a 3S 1800 ma 20C Sky LiPo