Discuss.
Indie Rock: the characteristic examples are Oasis, Kasabian, The Enemy, The Courteeners, &c.; the typical NME "lad band". Carling-indie, if you will.
Indie Pop: this encompasses C86, twee pop, and so on. Stereotypically a bit bookish, politically often left-wing (though not stridently political). The main difference from indie rock is that indie rock wouldn't admit to reading books.
Indie Folk: influenced by 1960s/70s bands influenced by British agrarian folk traditions, and/or recent American antifolk.
It's a bit like asking what distinguishes punk from metal. To an outsider, they're just people making harsh noises with electric guitars, though there are a number of stylistic differences, and more fundamental sociocultural differences.
I made a piece about this topic for "Loser Magazine" in the 80s. It was a print mashup of the gig guide and the real-estate ads. The gig guide is organized by music genre and the real-estate by suburb. Hence: http://spill-label.org/nw/lmag/genres.jpg
This was done in Sydney, so they're Sydney suburbs, which like Melbourne basically go from eastern/wealthy/techno via inner/indie to western/poor/rock. Unfortunately this A4 scan leaves out some of it.
A lot of Loser Mag / early New Waver was about class and the way it pops up in the music/arts scene in ways that, in the Marxist 80s at least, were embarrassing and not to be spoken about. For example, the cover of Jimmy Barnes' "Working Class Man" as "Middle Class Man".
Ok, I'll ignore the "correctness" of the graph and ask the bigger question/can of worms: What distinguishes Indie rock from Indie pop? (I am presuming we can all agree that Indie folk requires a beard and probably a youth spent in Missouri or something.