The various surfboard fin boxes
Overall, there are 4 different fin systems:
Futures:

Future is a relatively new system that is both powerful and easy. The fin is clicked in and fastened with a screw. The fin box is stronger than the other systems and is most often used for twin fins, as there is more pressure on the fins due to the larger area of the fins. But is now equally widespread on various thrusters, quads and 2 + 1 fin sets. The origins of Futures Fins took place in a garage in California in 1996. The Longo brothers had gained recognition for tackling challenging tasks in aerospace. But it was in 1996 that they decided to combine their technical know-how with something they loved. Surfing. They have always considered local production of the utmost importance, and now it allows Futures to conceive a fin, design it, cut it and surf it, all in a matter of hours under one roof in Huntington Beach.
Us Box:

The US Box is for single fins and makes it possible to adjust the position of the fin in the board. Some surfboards come with 5 fin boxes, 4 of which are either FCS I, FCS II or Futures and end with a US Box as the rear center fin. These boards with the possibility of alternative fin setups create fertile ground for really experimenting with your board's performance.
FCS II:

FCS II is a "click" system where you click the fins into the board, without the use of screws. This enables quick installation or removal of your fins. At the same time, this fin system has the advantage that if you are unlucky to hit the bottom, there is a greater chance that you will lose the fin versus destroying an entire fin box. However, it takes quite a bit to peel the fins out so you don't have to worry about losing your fins from time to time. The FCS II click system also enables the fin position of the singlefin to be adjusted while on the water. It is a popular system so there are countless different fin designs specifically designed for different types of boards.
Us Box:

FCS I, also called two tap, is the system that has always been on the market and a system that just works. The fins are mounted with 2 screws from the side with a small hex key. Gradually this system has been phased out and FCS (who developed the system) now produce very few new fin designs with the FCS I system.

SHORTBOARDS, Mid length & malibu's.
There are 5 setups for these board types:
Single-fin:

Single fins on the short boards are not that widespread - they are used on a few Malibu's and mid length boards, but are more of a niche thing in Denmark. Typically, a board with a shorter single fin requires a good, long wave – a la a point break that is not too powerful.
Twin-fin:

Found on retro fish boards, and seen more and more on performance boards up to 7'2 feet. Klaus from WestWind Vorupør only surfs on twin-fin boards, as he believes it gives a faster board and a more "loose" feel. There are 2 different twinfin models: "keel" and "performance". Keel is typically used on retro fish boards, which have a large, wide swallow-tail (the tips of a swallow-tail act as a small tracker – a small "extra fin"). Performance twinnies are for shortboards and boards with a more classic tail.
Thruster:

Setup where you have 3 fins of the same size. It is the most widespread setup, and is a real all-round setup that makes most people happy. It can be used on all boards from 5´- 8´. A thruster setup is almost also synonymous with high-performance surfing!
2 + 1:

Is the term for a Twin-fin with a stabilizer/tracker. The setup is good for those who want the feel of a twin setup, but lack a bit of hold. The setup is most often used on a classic shortboard. But many also have a lot of fun playing with this setup on more alternative shapes.
Quads:

The quad has 4 fins, for a better grip in powerful waves. The set-up is mostly used on spots such as pipeline - ie gigantic waves. If you have a board with 5 fin-boxes, we recommend that you try a little to see if you are more into quad or thruster.
LONGBOARDS are boards between 9-11 feet.
They are rounded in the nose and can be used in even the smallest waves.
When choosing fins for your longboard, there are a few rules of thumb that are good to know. In short, the small fins are better suited for turns and maneuvers, while the larger fins provide better stability and are ideal for noseriding.
When you need to find the ideal fin length for your longboard, you can use the rule of thumb: Take the length of the board and replace the unit (feet) with inches to get the ideal fin length. If you have a longboard of 9 feet, you can therefore advantageously go for a 9" fin. 10 feet = 10” etc. The position of the fin also affects the characteristics: the further forward you place the fin, the better turning characteristics you give the board. If, on the other hand, you move the fin further back, you will create more speed.
A short fin for maneuvers is often combined with some side bites (side fins), which ensure more "grip" during turns.
Cutaway Single Fin:

This fin is suitable for smaller single fin boards – 6–8 feet. It is often used on shorter pintail boards (board with a pointed rear end) and it is used without side bites.
Large Pivot fine:

This fin is a large Pivot. It is perfect for noseriding and provides a stable board. The larger area makes it suitable for the heavier surfer as well as the larger longboards. An 80/20 fin – 80% noseride, 20% maneuvers.
Classic Hook/flex fin:

This fin is a classic "Hook" model. An all-round fin that fits most things. It is a manoeuvrable fin that is less suitable for noseriding. A fin like this suits many surfers – the safe choice.
Classic Pivot fine:

This is a Pivot fin which is good for noseriding. The relatively small area of the fin means that it is better suited to the light surfer and to the smaller longboards. A fin like this is 70/30 – 70% noseride and 30% maneuvers.
D fine:

A large, heavy fin that fits very well on old school longboards and for classic surfing. It is 100% noseride and glide – a real cruiser.
There is more theory than practice in fins, so spend the time on the water”
– Klaus Sørensen, WestWind No. Voruper