Except for when riding deep stuff, the influence in riding is not that big (even for that, the offset stance setback has much more influence), so much people just chose a cool shape that they like. That being said, we can proceed.
The nose and tail of the snowboard come into play when riding powder, slush or mixed conditions and when popping ollies and nollies. Their size and shape will have influence in those situations.
Normal round nose and tail
The typical one (or maybe not so much anymore), for a long time it was the only one and have always worked just fine.
Smaller, starighter nose (Blunt nose)
More control and less energy spent, because of less swing weight
You can ride a smaller size with the same control, because with the same snowboard size it has more effective edge than the normal nose.
Easier nose/tail grabs and fewer hook-ups on rails, because of the smaller board size that'll make
Sinks easily when below the surface (in powder) because by being smaller the nose also becomes lower and flatter, but float well because of its large surface.
Sinks less and floats more in powder, slush and mixed snow conditionsbecause it's more curved and has more surface (the front of the board gets bigger).
The snowboard noses tend to get pointier when they get bigger. A big wide nose will float more but with more weight, more swing weight and less control. Can be nice on short powder boards.
Pointier nose (straighter shape)
Less shattering / more control, because it cuts better through the snow, even smaller noses.
A pointier nose saves on weight while adding size, and because it doesn't add that much swing weight and because of the shape itself (that helps controlling your direction on fluffy powder, much like the point of a surfboard does in the water)will float more and more precisely in deep powder.
Strictly for powder sticks. The swallow shape helps with spreading your weight keeping it in the center of your back foot, and it works a bit like fin in a surfboard giving you more precision. Is usually flatter, making riding switch an impossible thing. Also helps the tail to sink, like a pointy tail or a short one.
Pointy tail / Short tail
They will help the back of the board to sink.
A pointy tail gives you a bit more precision, like the surfboards fins, as does the swallow tail.