Generally speaking, you'd be correct to think that the bigger the number, the bigger the spool. However, it's not necessarily quite as straight forward as that and there are strange anomolies even within a single manufacturers range.
Shimano seem to have two different size scales. Match/Smaller specimen reels that go from 1500 to 10000 size with 2500, 3000, 4000, 5000, 6000 and 8000 in between. Then there are the mini/big pit reels that go from 4500 to 14000 with 5500, 6000, 7000, 8000, 10000 in between. A 4500 mini pit reel is huge compared to a 5000 size standard baitrunner.
It's also worth noting that many of the reels of different number designation have exactly the same sized reel bodies with different size rotors and spools. Sometimes the dimensions are just the same and just the line capacities of the spools change. Occasionally you'll find 3000 and 4000 sized "match" reels have shallow spools of bigger dimensions but smaller line capacities than 2500 and even 1500 sized reels in the same range.
As to your barbel/carp reel, what rivers are you fishing? What sort of weight are you expecting to chuck about? If you are going to try chucking 4oz plus feeders 40-50 yards then you may be well served getting a much bigger reel. Much of my barbel fishing uses 4/5000 sized baitrunners. However, carping and barbel fishing on the Trent sees much bigger reels come out to play.
mg: