When you say, "Merry Christmas," or "Happy Birthday," there is a coherent meaning to those words. You are wishing that the person you are talking to will have a merry/happy/joyous day on the occasion in question.
When you say, "Season's Greetings," all you are doing is mentioning that there are a number of greetings one uses at this time of year. It does not indicate that you are expressing those greetings, merely that you affirm that they exist.
In short, it is totally fucking meaningless.
At least, "Happy Holidays" is a form of well-wishing. Whatever holidays at this time of year that one celebrates, I hope that they are happy for you.
When you say, "Season's Greetings," all you are doing is mentioning that there are a number of greetings one uses at this time of year. It does not indicate that you are expressing those greetings, merely that you affirm that they exist.
In short, it is totally fucking meaningless.
At least, "Happy Holidays" is a form of well-wishing. Whatever holidays at this time of year that one celebrates, I hope that they are happy for you.