"To say" is simply to speak; to have words coming out of your mouth at some audible level. "To tell" is to communicate a thought to some listener.
There is thus a slight grammatical difference; "to tell" requires that the object be the listener or recipient, and what is/was communicated becomes the object complement. With "to say", what is said is the object, unless a preposition is used to insert a listener as an object.
So, the following are all valid:
I said, "go away". - (no listener specified; it must be implied from context)
I said to Tom, "go away". - (listener specified as a proper noun)
I said that Tom should go away. - (Listener not specified, despite the presence of an object noun; it is part of another statement joined to "I said" with a conjunction)
I told Tom "go away". - (listener specified, implication is that Tom received and understood the message)
I told Tom to go away - (listener specified, what is told doesn't have to be a quote)
However, neither of the following are valid:
I said Tom "go away" - (requires a preposition to insert an object noun)
I told "go away" - (requires an object noun and object complement structure)