Difference between "Becoming" and Anicca To preface my question, I will add that I am very unfamiliar with Buddhism.  My knowledge consists of some historical anecdotes, and I also know some of the basic tenets.

That being said, is there a difference between "Becoming" and Anicca/Impermanence?  The former is a philosophy that originated in the West, and is nearly as old as Buddhism itself.  Are they essentially the same thing, but stated differently?  Or am I overlooking a huge fundamental difference which delineates the two?
My answer assumes you are specifically referring to the ideas of Heraclitus (the originator of Western ideas of Becoming). There are some interesting correlates between the origins of the Western idea of flux or becoming which was first articulated by the Greek philosopher Heraclitus and the Buddha's idea of Impermanence (Anicca). For Heraclitus ...


  Everything flows and nothing stays.
  Everything flows and nothing abides.
  Everything gives way and nothing stays fixed.
  Everything flows; nothing remains.
  All is flux, nothing is stationary.
  All is flux, nothing stays still.
  All flows, nothing stays.
  
  No man ever steps in the same river twice.


There is subtle distinction between the Buddha and Heraclitus on the mechanism of change. For Buddha the process of change is driven by dependent origination - the idea that every phenomena exists entirely dependent on the causes that proceed it. Heraclitus had more of a transformative concept of change - that phenomena are the result of the tension and flux of the opposites. The end result is the same however - constant change. 

So essentially there is very little difference between the Buddha's concept of  Annica and Heraclitus's ideas of Becoming.

Other interesting similarities between Heraclitus and Buddha:


Both were born into aristocratic families and were first in line to inherit.
Both rejected their inheritance and chose rather to pursue a life of contemplation instead.
Both their philosophies rejected the prevailing eternalism of their respective cultures and chose rather to rely on reason and personal experience to arrive at the truth.
They were fairly contemporaneous with each other - Heraclitus (c. 535 – c. 475 BCE) &amp; Buddha (6th century BCE)


There are many articles and books dedicated to investigating the similarities between the views of Heraclitus and Buddha on the internet. Nice summary here -  Heraclitus and the Buddha on Impermanence