Is it Argentine, Argentinian or Argentinean?

Before coming to Argentina, I was as sure as one could possibly be, that people with a residence of Argentina are Argentinians. Then I heard many people using the word “Argentine” and I read about “Argentinean” music. I got very confused and tried to understand the different meanings and usages. However, every theory I made up on how to use the different words, was falsified within houres, leading to a big uneasiness whenever I should describe someone or something from Argentina with an adjective.
After months of avoiding to refer to “Argentinians“, afraid to make a fool of myself, the Elebaires staff explained me during an afterclass activity of my spanishcourse, that there is no significant difference between Argentine, Argentinian or Argentinean. The very slight difference in the usage is dismissable in everday language.
Puh! What a relief! I went back to talk easily about Argentine wine, music and food…until the word “Argie” pops up. Does anyone know how to use that word?
Please tell me in a comment!