Usually when we use “to say” we are referring to what was actually spoken. “To tell” refers to what the information was. What did he say to you? (Means what words did he actually speak to you) What did he he tell you? (Means what information did he tell you, not specifically the actual words) So you can say, I hear what you’re saying but I don’t understand what you are telling me.

As Matt says, but also to just clarify something he said somewhat indirectly: to say, does not imply that you are listened to, to tell, generally, has more of a sense of communication working than say. To tell does not always impy that the message was received, but more so than "say".

I think "They said to each other." is not a complete sentence. Usually when you use "say", you have to include the thing that is said in the sentence. You "say something [to someone]". I guess this is because the natural emphasis in the verb "say" is on the fact of words being pronounced aloud. "They told each other." - this could be a complete sentence, in the right context. For example: "Who told John and James that they looked as if they had gained weight during the lockdown?" - "They told each other." When you use the word "tell", you normally have to specify the audience in the sentence, so you "tell someone [something]". There are exceptions though, or different uses of the word "tell". You can "tell a story", "tell a lie" or "tell the truth" (without specifying the audience), or you can use the word "tell" with the meaning of perceiving or understanding something, e.g. "he hasn't learnt to use a clock to tell the time" or "I can't tell if you're lying or not". Maybe the usual idea with "telling someone something" is that when you "tell" someone something you inform your audience of that information. In that sense, telling is the giving of information, rather than the pronunciation of words. So the identity of the audience normally needs to be specified. However for example the sentences "he said to her that he wanted to go to the cinema with her" and "he told her that he wanted to go to the cinema with her" are fundamentally identical in meaning, they just follow slightly different grammatical rules (to say something [to someone], to tell someone [something]).

Eric Lin has explained it perfectly. Yes, while both sentences or phrases are grammatically correct, using the word say/said means you're pointing out to the actual words spoken. Tell/told gives more importance to the message of those words.

They said to each other is usually followed by a dialogue quote of the exact words which were said, while ‘they told each other’ is used in a narrative speech where someone is retelling the story. Hope this helps 😊