The real difference between say and tell is in their syntax. Both are transitive, but tell is obligatorily bitransitive -- it requires an indirect object and usually takes the Dative Alternation:
- He told his boss what it was.
- ?He told what it was to his boss.
- *He told what it was.
Say, on the other hand, takes only a direct object, no indirect object:
- *He said me what it was.
- ?He said what it was to me.
- He said what it was.
I use an embedded question object clause what it was in the examples above, but there are several other possibilities for each verb. Both can take direct quotes, though they are more frequent with say:
- He told me "You have the right to remain silent".
- He said "You have the right to remain silent".
Both can take that-complements:
- He told me (that) I had the right to remain silent.
- He said (that) I had the right to remain silent.
Both can take infinitive complements:
- He told me to stay silent.
- He said to stay silent.
With an infinitive complement, both say and tell are interpreted as giving orders or direction, rather than stating. Moreover, the dativeless say produces an infinitive with an indefinite subject, thus allowing the interpretation of giving general instructions.
Their nominalization potentials are different, too. Tell, but not say, can have a noun direct object that describes the content of the message:
- He told me the condition of the manuscript.
- *He said the condition of the manuscript.
while say, but not tell, can have a noun direct object that describes the speech itself, rather than its content:
- *He told me the N-word.
- He said the N-word.
So, as with most closely-related pairs of common verbs, there are a lot of similarities in their syntax (and why not? they're mostly used for the same purposes, after all), and some differences, too (again, why not? they wouldn't be two different verbs if they were identical in every respect).
One difference is that tell focusses on the indirect object (the addressee, and therefore on the social aspects of communication), while the focus of say is certainly not on the addressee, but rather on the direct object (the message).
Another difference is that, while whatever appears as the direct object of tell may be a paraphrase of the message, the direct object of say is the message itself.
Hence one might reasonably expect the information in the object of say to be more exact or precise a rendering than that in the direct object of tell. That's not saying there's a truth difference here, understand; anybody can lie and anybody can report any statement.
What I mean is that tell seems to occur in situations where paraphrase is generally sufficient more often than does say; and also, possibly, that say occurs in situations where paraphrase is not sufficient more often than does tell.
This is impressionistic, I'm afraid; I've conducted no surveys. But it's consistent with the syntax. When you get down to the fine details, every verb is different from every other verb not so much in meaning, but in its syntactic affordances and prohibitions, which, taken together, constitute a large part of what we laughingly call its Meaning.