Talk To Me Like I Am Stupid: Communist Deviations

For those following along, I'm about two thirds of the way into Anne Applebaum's The Iron Curtain. I'd like to submit myself before the the tender mercies of the Horde and ask for some help. Specifically--how do we define a "right deviationist" and a "left deviationist" in communism? As I recall this has something to do with the decision to pursue "communism at home" or push for a world revolution, but I'm not sure which. More I'm not sure how each can be married to either end of an ideology.  Perhaps more confusing, much like the term "kulak," (or even "Jew") at some point these labels lose their meaning and just become slurs to hurl at enemies. Still, I'd like to be able to at least follow the logic. 

Help me mighty Horde. You're my only hope.

As with all of these threads, one could easily google this. But the knowledge that comes from an active back and forth will always be superior. In that vein, please don't do a quick google or wikipedia so that you can yell "First!" If you don't know, just wait. Someone who does will post soon enough.