We never think about the definition of those phrases. They're just phrases. You could probably try to understand what they really mean but most native speakers don't. Best Regards: This is most likely something like "I wish you the best". You are saying you hope things go well for them. I think "best regards" used to be used like "goodbye". Sincerely: The word "sincere" means to be honest, truthful, and normally serious. It means you're expressing your genuine feelings. So when you write "Sincerely" at the end, it means that you really mean everything you said in the message. Like I said, most native speakers never think about what these phrases mean. I could be wrong about the definitions I gave, they're just my impression.

Best regards is shorthand for saying I wish you all the best ( I am hoping everything goes well for you) I am old so I remember when all business(formal) letters were ended with the words ... "Yours sincerely" followed by your signature.. Sincere means you are being truthful and honest and mean what you say. It was a courteous way of finishing, like bowing as you left the room - only in writing. In older times they would finish .. " I am , Sir, Your obedient (or humble) servant....

There are rules governing the use of these forms of signing off a letter. A learner should learn these rules. If you open with Dear Sir, you must end with Yours faithfully. This is the most formal form. If you open with Dear Mr. Brown, you must close with Yours sincerely. "Best regards" is the most common form of signing off an email now, but do not use it in a letter. There is no need to learn or use any other form though you will see.people use them. They are not regarded as standard. None of these mean anything at all. It is just just established protocol to use them according to the rules. Don't ask why. It's just like a soldier's salute. Tradition. Protocol.

I think of them as very nice and formal ways to say goodbye. These phrase are usually used to end a letter, especially "sincerely yours." You could also say "yours truly."