The first obvious difference is the single fin runs through the water easier than a multi fin board.
Since there is only one fin set at 90°to the bottom shape and sitting parallel with the stringer, these two factors minimis the drag aspect of the fins function allowing the board to pass through the water with minimum drag opposed to all the multi fin set ups where all side fins are set at an angle to the stringer both fins towed in to wards the nose and also splayed out to the rail.
This in turn causes the fins to plough through the water creating more drag than the single fin set up. This can only be relived when the board is turned constantly.
Example of a hull shape (surfboard bottom) repeated five times exactly the same, leave one with no fin and then a single, a twin, tri fin and four fins put them in flat water and line them up then give them all the same thrust from behind. The board with no fin will run the furthest followed by 1 then 2 fin then the 3 and finally the 4 fin set up.
Why? Simple, drag added to the hull, no fin no drag, as each fin is added to the hull so the drag factor increases.
It really is simple logic when though about.
How does this effect performance?
Quite dramatically in terms of performance, regardless of hull shape the fin set up determines the style of performance obtainable and there is a correct way to surf the various set ups as each one needs to be surfed differently to obtain maximum performance.
In terms of performance keeping it simple.
Hulls with side fins will rotate from rail to rail and with side and centre fins a quick short burst of speed is the effect, more a stop start performance.
The single fin gives smooth longer arcs with more overall flow and if the rails are designed correctly through the tail area much greater control in the hollow parts of the wave, tubes and steep walls.
When contemplating a surfboard design keep in mind that each fin combination will surf differently from the other and each combination requires an individual approach to how best to surf the board.
It is not a matter of which design is best, it is a matter of how you wish to surf.