They all mean GOODBYE. They're said when you leave somebody. FAREWELL is old fashioned. I'm not a young man and I've never used it in my life. BYE, SEE YOU, and SO LONG suggest you'll see each other again.

See you = see you again later or another time, more for we'll meet again... bye = good bye, more for sending off a visit... farewell = more for longer seperation like going overseas so long = close off, meaning "that is it, is long enough that we should end here" All are similar and interchangeable use except for farewell which usually usually use in longer separation.