Put simply, all Cognacs are Brandy, but not all Brandys are Cognac.  Still a bit confused?  That's a sure sign that it's a French thing.  In order for a Brandy to be a Cognac it must come from the Cognac region of France.  Everything else is Brandy.  Brandy and Cognac are made by fermenting and then distilling grape juice.  Cognac has very strict production and labelling rules to protect it's quality and reputation. Most Cognacs are not a "vintage" product.  They are made up of spirit from many vintages and the class of Cognac is determined by the youngest spirit in the blend.  Cognac must be at least two and a half years old starting with the first of October of the year the grapes were produced.

The classes and rules are as follows:

V.S. (Very Special)  The youngest in the blend must be at least four and a half years old and stored for two years of that time in cask.

V.S.O.P. (Very Superior Old Pale) also called Reserve, The youngest in the blend must be between four and a half and six and a half years old with minimum four years in cask.

X.O. (Extra Old) also V.O., Napoleon, Imperial, or Hors d'age are a minimum of six and a half years old with six years in cask.  Many Cognacs and Brandies with these designations contain spirits that are fifty to over one-hundred-years old                                                                                                   
In addition other notable terms are put on a Cognac Label.
"Fine" when used on a label as in "Grande Fine Champagne" signifies that 100% of the grapes used were from the Grande Champagne Region.

"Fine Champagne" means at least fifty percent of the grapes were from Grand Champagne, the balance would be from the Petite Champagne region.

"Fine Petite Champagne" or "Petite Champagne" means that the grapes were all from the Petite Champagne region. 

These are the main regions of note for Cognac.  There are other lesser appellation designations that are considered lesser quality than those listed.  Brandy is made from grapes of other regions, Armagnac is one example.  Brandy can also be made from Apples (Calvados), Cherries (Kirshwasser), Plums (Slivovitz) or other fruits. In closing, Cognacs and Brandys are usually better enjoyed chilled rather than heated as the proliferation of Brandy Warmers would suggest.  Chilling tempers the spirit making the alcohol less harsh on the palate.