Jib
A jib is a triangle sail that is forward of the mast.
They have a number of names, some of them refer to their percentage of overlap, of the mast.
If the aft edge of the jib reaches back to the mast, then it is a 100% jib, also known as a working jib.
If the 10% of the jib extends aft of the mast, then it is called a 110%.
If it has 135-150% aft of the mast, it is commonly called a Genoa.
The very small ones that do not extend aft to the mast are called storm jibs.
The jib typically has 2 sheets attached to it's clew, the tack is attached to the bow or a sprit, and the head is hoisted with a halyard.
Jibs work better with very high luff tension, this helps form the right sail shape.
Staysail
A staysail is a jib which is flown between other sails, such as between the main and the jib.
Spinnaker
These are very pretty sails and can greatly increase your speed going down wind.
There are several versions, the one pictured is a symetrical spinnaker.
They are typically flown free off the bow of the boat, one sheet on the clew, and one on the tack.
The halyard has a swivel on it so when hoisted, if the spinnaker is twisted it can unroll itself.
There are a number of variations of a spinnaker, the most popular being an asymmetrical.
It is more like a very large genoa, having 2 sheets on the clew so it can be tacked like a jib.
The asymetrical is able to go at greater angles than the symetrical, which is mostly good for straight down wind.
Some of the other names for the spinnakers are: spanker, cruising spinnaker, chute, reacher, drifter, blast reacher, flasher
Mary Poppins Spinnaker
Simplest of all sails, the umbrella.
Many kayakers use umbrellas for sailing down and cross wind.
The trick to using them is to tie strings from the tips of the umbrella back to the handle, this will prevent the umbrella from blowing inside out.