I happened to see the word Aussie and knew it means Australian. But is there any different implication of these two words, Aussie and Australian? Thanks
There are no positive or negative implications. It's not rude or impolite.
As a noun, it's used for people. He's an Aussie.
As an adjective, you generally only use it attributively:
He likes the Aussie way of life. But NOT His way of life is Aussie.
Aussies pronounce it /ozi/, unlike many Americans.