Icon -- Originally, a religious symbol of one kind or another. It's since also come to mean an emblem or symbol.
Iconoclast -- A person who attacks the established order of things. It can also mean someone who attacks religious images -- or icons. It's east to see how the word attains its current wide usage, generally referring to someone out of the mainstream.
Thus, if someone says a painting or song is iconic, she means that the work of art has come to be symbolic -- representative or an era or a standard. If something is described as iconoclastic, that means its something that goes against the icons of a culture. That "oclast" puts the two words in opposition.
It pained me to hear a radio host refer to a song as being "iconoclastic" awhile back. He was speaking about "Somewhere Over the Rainbow," the song by Harold Arlen and Yip Harburg that came to represent both the movie it came from -- The Wizard of Oz -- and the performer who sang it -- Judy Garland. The song could thus be called "iconic."
That's that.