Official faction = group of indies that <strike>like to order each other around</strike> follow faction RP
Later.. of course members become friends and rank structure is there only for the sake of RP, they decided to build up on that RP too, made some agreements/alliances, broke some, exchanged technology and took their future in their own hands and now don't like anyone to brake what they did or what others before them did (now they have rights to keep it that way). (They can change things as long rest of the community agrees of course)
Indy = One person, can't do much to change future of his faction, or make big impact on community. Unless they are willing to spend much time on their RP that makes some sense and turn it to something wonderful (It has been done before - there are few unique ships, chars)
Some spend some time as indie and join faction, no matter how good or bad they are if they have willingness to join they will.
Some are just there for fun on their own and they don't make trouble, they follow faction RP and generally have fun.
There are those that like to form their own groups.. well you aren't really indie more, they are making their own rank structure etc.. they become unofficial faction (sub-faction or what ever) some even turn to official factions if they last long but usually these groups don't live long and brake up soon.
I am not sure, but I don't know why so many guys decide to made their groups that are basically same as official faction and do same things.. they could simply join it and form their own wing in it, recon, defensive, scientific, etc. It's much better option if you ask me, this is just my opinion. It would last longer and with official faction you could build up factions RP and contribute to something. If you are already making group why not bring it to next level.
And there are indies that are generally new, have little knowledge about factions lore and want to have fun, and they usually mess things up, it's on them if they want to straighten up or get sanctioned. You can't really blame them, we were all newbies once. Even the newbies newbie will get straighten up after talking with them, teaching and if that fails sanctions will do the trick to lead them to correct path. Usually talking is enough.
Some newbies form groups that still have little knowledge about faction and get FR5'd for doing stuff wrong.
Finally Some of those won't even admit they were wrong, they don't want to follow rules and they turn into trolls
Oshi.. wall of text. So, my general view of faction-indie stuff 30 mins after I wake up.