Coming from a sailing background rather than a surfing background I have never fully understood the nuances of the board and fin. Call me a nincompoop but it was only last season that I realised with foot pressure you could steer the board Thick as a Brick - I know
Well yesterday I tried a smaller fin on my board and boy did that change things dramatically.

I have a 144 ltr board with a 50 cm fin and when the wind comes up over 15 kts it gets a little uncontrollable. So I went and purchased a 40cm fin.

First tack the board was so responsive I spun it on a sixpence and ended up in the drink at 10 degs thank you very much. I could feel the board responding to even the slightest weight shift in the feet.

However when the wind dropped I found myself crabbing across the water.

Can the tech heads out there explain to an old dog learning new tricks why 10 cm in fin length makes such a huge difference, why I was crabbing and what else should I be looking for/doing?

Well it's a 20% change, same as going from a 5.0 sail to a 4.0 quite a big change.
As you slow down, the smaller fin isn't producing enough lift to counteract the sideways force on the sail, so you crab, increasing the angle of attack of water on the fin, which increases it's lift. Push this too far and you'll just spin out when the fin stalls.

Board response is about fin leverage over the board, the longer the fin the more leverage it has, making it harder for you to tip it over, so decreases speed of board response to weight changes.
I think there's also an element of tail sliding in turns, the bigger fin is going to do this less as well.

Coming from a surfing background, here is my opinion of what a fin does when you are turning:

When you carve, you are using the bottom of the board as the main lifting surface. The fins are merely there to stop your board skipping sideways out of the water.

Yep, a bigger fin is not as loose because it makes it harder for you to change the angle of attack of the bottom of the board.

Small fins have less lift compared to big fins, making it easier to push the tail sideways, giving a greater angle of attack of the bottom of the board to the oncoming water, giving you a smaller turning radius.

It is not the fins that are doing the turning, it is the bottom of the board. (same as with a kiteboard)

What Thrusters Do:

The less fin that is in the water while you are turning, the more prone your board will be to spinning out. This is not because the fin is turning the board, but because the fin is holding the board in the water. If the fin can't hold the board in the water, the tail will just slide sideways (unless you have really good control of your board).

To minimise sliding out, the single fin solution is to have a really narrow tail and a really long fin. Narrow tail keeps the fin close to the rail of the board, and hence, close to the waterline.

Thrusters solve this problem by putting side fins close to the rails of the board, allowing you to have a nice wide tail for planing purposes.

I'm not sure as to the reason why the side fins on thrusters are toed-in though. You'd think that this would lift the board out of the water when you are turning. Maybe it allows you to slip down the face of the wave a bit, rather than biting in and dragging you up the face?