The meaning is almost the same. "Nashle" is a colloquial expression for "Na shledanou", it is a little bit less polite. "Na shledanou" is a formal expression, which you can use in shops, institutions, work, etc. They are both used (mostly) in spoken language to people that you do not know very well.
If you wanted to say "Bye" to a friend, you'd probably want to say "Ahoj" or "Čau". These are used for saying both Hello and Bye, but I think the contributors wanted to use also other expressions.