"Told" vs. "said to" somebody

The main difference is the use of objects. 'Told' can only be used as a transitive verb. 'Said' can be used either way, but is most commonly used in the intransitive form. Personally I've only seen the transitive form used with a direct quotation, as illustrated below.

I told him the moon was made of cheese.

I said the moon was made of cheese.

"The moon is made of cheese," he said to Mary.

I would never say, 'I said to him the moon was made of cheese.' It may be grammatically correct, but it's awkward.

The only other difference is that 'told' has an idiom:

I told you so!

You would never say: "I said so to you!" You might in some cases say: "I said so!" but it doesn't carry the same tone of rebuke.

The Oxford English Dictionary has numerous definitions and citations for both verbs. I don’t think we can conclude that tell implies a lie and that say doesn’t. The sentence I told my wife it wasn’t lipstick on my collar might well contain a lie, while I said that I’d been unfaithful to her might be true.

Enlarging a little on what Lynn has said, in grammatical terms, the difference is a matter of valency, of what other words can follow each verb. Tell is ditransitive, that is, it can take a direct and an indirect object, as in I told him a lie. Say, on the other hand, is monotransitive. It normally takes a complement clause as its direct object, as in I said he was lying, but occasionally a direct object is possible.

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.

No. There is no difference in the normal sense between told and said to. Either one can be true or untrue. But, it sounds better to simply use told, in almost all normal cases.

Said can also be used with a passive voice such as "it is said that the moon is made of cheese", which makes this device is useful for saying things that are untrue or unproven, because it avoids naming the subject. ("It is said" means some people say it, not "I said", so you can't accuse me.)

I think you're not alone in concluding what it implies. There is a difference between ‘to tell’ and ‘to say’. Apart from the dictionary definitions, common use indicates this blatantly, there is a difference in intention and content.

To tell is to inform or be imperative.
To say is to utter or express something; it's more general.

Examples

I told her that I would be here at 8:00. — Factual.
I said to him “wham, bam, thank you, mam!” — Not factual, nonsense. ‘Told’ isn't used here.
I told her not to sit there. — Imperative.
I said to him “It was not death, for I stood up, And all the dead lie down....” — Not factual, poetic. ‘Told’ isn't used here.
I said to her, “I love you.” — Factual.
So I said, “hurrah!” — Non factual, interjection. ‘Told’ isn't used here.