"Way" tends to represent a course of action. There is only one way from point A to point B. http://www.merriam-webster.com/dictionary/way "Manner" tends to convey the mode (average way) in which something is done; follows a rule. http://www.merriam-webster.com/dictionary/way The "manner" in which it is done is not always the same. The "way" we do things is always the same. They are nearly the same, however "manner" tends to be more formal.

Coming from Old English, the word "way" is more common. "Manner" comes from Latin via Old French, and so it has more formality.

Please use the word in a sentence. There are many definitions to both.