Re: How does coral grow?

Corals form large colonies of many animals by asexually reproducing 
(cloning) new individuals on the edges of the colony, or on top of older or 
dead parts of the colony.  A small portion of an individual coral (polyp) 
can "bud" off and become a new individual right next to the original.  This 
new coral polyp forms a skeleton around itself that is fused with the 
skeleton of the polyp it came from and those around it.  Over MANY years, 
these tiny animals can form a HUGE reef structure as polyp upon polyp 
(along with their skeletons) get added to the colony.  As the corals die, 
they leave their skeletons behind, which can them be grown over by new 
corals, etc.  These layers of skeleton can make massive mounds and 
structures which form the coral reefs in the tropical climates where they 
live.

You are correct that different forms of coral are different species 
(usually*).  Why a particular coral grows in the pattern it does, I'm not 
totally sure.  My guess would be that each coral species has a certain 
budding pattern that dictates what direction a new polyp will grow relative 
to the one it came from.  In brain coral, buds may just develop directly to 
the side of the "parent" polyp.  In Staghorn coral, the bud may develop 
more towards the oral end of the "parent" polyp, thus forming a more 
stick-like structure as polyps "climb on top of each other's shoulders" so 
to speak.  Another possibility is that the shape of their skeletons that 
they form around themselves, when stacked together, dictate the shape of 
the colony.  Staghorn skeltons, being somewhat cone-shaped may naturally 
lend themselves to forming stick-like structures when stacked together.  
Whereas brain corals, having more flat, disk-like skeletons, may fit 
together better if you lay them side by side or on top of each other.

* Staghorn coral is certainly a different species than brain coral, but 
sometimes one particular coral species can take on different shapes 
depending on what will work best in a particular environment.  For example, 
a colony may be tall and slender in calmer waters, but another colony of 
the same species may be more flat and streamlined in an area with more wave 
activity (which would break apart the more fragile slender form).  To my 
knowledge, almost all corals have the ability to adjust their growth form 
based on environmental conditions, but some do so more than others.