Tequila's Origins- By Mexican law, a tequila is a tequila if only if, and only if Blue Weber is used (no less than 60%, though you never know when the Mexican government might change this) and that Blue Weber was grown in one of five states in Mexico designated as tequila producing states.

Types of tequila- As defined by the Mexican government, there is MIXTO, an alcohol distilled from no less than 60% blue agave.  The rest is other juices, most typically sugar cane.  100% Blue Agave is, well, 100% Blue Agave.

Aging-
There are 4 age designations:
Silver (also called Plata and Blanco)- bottled no longer than 60 days after it was distilled.  A clear tequila.
Gold (also called Oro)- Same as Silver, but made gold colored through adding caramel (usually).  This softens the tequila a bit.
Reposado- meaning it has "rested" for between 2 months and a year in a barrel. 
Anejo- Aged in small wood barrels (often casks once used to make Bourbon) for no less than 1 year.

FYI- There is no worm in Tequila.  Sometimes there is a worm in mezcal, another distilled beverage made in Mexico, but never in Tequila.

Speaking of Mezcal-
While also made from Agave, Mezcal is made from any of eight particular Agaves, including Blue Weber Agave.  Very confusing, no?  So yes, a 100% Blue Agave alcohol may be either a mezcal or a tequila.  If it was made within the 5 designated tequila states, its a tequila.  If not, it is a mezcal.

Often, mezcal is looked down upon by tequila patrons  because it is not made in the 5 tequila states, which are known for producing the best Blue Weber Agave plants, and because it may be up to 40% derived from sugar cane, which usually makes harsh, not spirits.