What kind of board do you want/for what kind of conditions? Honestly, if you are still new enough to surfing that you don't know what each is for it probably doesn't matter much for the time being.
That was my smart alec answer....answer to your question is:
Pin tails
Pin tails are usually used on big wave boards as they are designed for down the line speed with trimming in mind; mainly used in freight train waves.
Boards suited for this tail – guns (big wave boards).
Rounded pin tails
The Rounded pin is looser than a pin tail allowing the surfboard to do smooth transitions though still keeping the speed of the pin tail for bigger waves. This also makes the board quite stable.
Boards suited for this tail – short boards suited for bigger waves, fun boards (mini mals and some Malibu surfboards.
Round tails
An ‘all round’ performance shape used in most surf conditions. This tail design gives you the smooth transition but the tighter turning arcs.
Boards suited for this tail – performance short boards, fun boards, retro boards, and small wave boards.
Square tails or squash tails
The most common modern surfboard tail, it’s quite responsive in turning but helps keep the speed through the fat sections of the wave.
Board suited for this tail – performance short boards, fun boards, Malibu’s, hybrids, small wave boards.
Rounded square tails
A Rounded Square tail combines the performance of a round tail and a square tail, great all round performance for most types of waves.
Board suited for this tail – performance short boards, fun boards, Malibu’s, hybrids, small wave boards.
Swallow tails
Swallow tails are excellent for controlling sharp turning arcs because of the wider tail area and larger planning surface.
Board suited for this tail – performance short boards, and fish style small wave boards.
Fish tails
Designed with the small wave in mind, with the less push in the wave the fish will keep planning longer helping you do turns.
Board suited for this tail – retro boards and fish style small wave boards.
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More on Surfboard Tail Shapes here)