Goodbye, like hello, has many alternative words and phrases which mean the same thing.  Goodbye could be classified as formal, but it is the kind of formal that you can use in most situations, casual and formal, and not worry whether it is appropriate or not.  The variations of goodbye are the product of youth culture slang, regional dialects and even foreign languages which have filtered from a subculture or group into mainstream conversation.

ways to say goodbye

 See you later, see ya later   ‘Ya’ is used in American English and is more casual than ‘you’

 See you soon, see ya soon    

Take care  This is used when you care about the person you are saying goodbye to.  It is used in written English as well.

Take it easy   It means ‘take care.’

Gotta go     This is a hasty goodbye used by someone in a hurry, an effort to be polite despite wanting to leave.

Talk to you soon or Talk soon  Used in phone conversation or in emails, this is a casual way to saying goodbye to someone you probably have a lot of contact with.

Catch ya later     This is a casual goodbye.

See you later    As above

Later     This is also a casual goodbye, and its really only used by youth, college kids etc.

Have a good one     This can be used with anyone and it means ‘have a nice day’ and its used in casual situations.

Have a good day    This is used in more formal contexts, such as in stores as you leave, between a customer and a host, a client and a company representative.

Then there is just plain old ‘bye’, the most common way of saying goodbye in English. You can use it anywhere, and with anyone.  Finally here are a few ways that English speaking people say goodbye, but in a foreign language.  Most popular foreign language goodbyes are adios (Spanish), ciao (Italian), and au revoir (French).