Formal Definitions:
Arrancar: Hollows who have had their mask removed (forcibly or not) and gained the ability to transfer into a stronger hollow form by releasing their zanpakutou.
Numero: Usually Menos that were turned into Arrancar and are numbered according to their order of creation (this idea has all but been abandoned).
Fraccion: A numero, arrancar, or even a high level arrancar (usually not an espada) that has been chosen to serve an espada. They can be stronger than Numero, most other hollows, or even the same level as some of the current espada. The equivalent of seated officers/lieutenants.
Privaron: An espada that was kicked out or replaced by another who is stronger than most other hollows, but can be weaker. Dordonii, Gantenbeinne, Cirucci, and even Nel fit this description. Their numbers are equivalent to their former strength but does nothing to indicate their current strength when weighed against other Espada.
Espada: The 10 strongest Arrancar, arranged in order of strength or ability. Nnoitra, for example, had tough skin, but didn't appear substantially stronger than Grimmjow, who was able to hold his own against Ulquiorra for a brief time. They are the equivalent of Captains. Most of them are stronger than the current captains, with the top 4 being speculated to be the strongest. Yammy's been forgotten about, since he's Espada #10 and at his current level all of the major characters could kill him.
Arrancars are either formed when using the Hougyoku (wonderweiss) or when having their mask ripped off (grand fisher). The transformation, like the Vizard transformation, cannot be reversed.
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