The boy is standing at the desk. <-- implies he is at the front of the desk The boy is standing at his desk <-- implies standing behind the desk, instead of sitting in his chair The boy is standing beside the desk <-- implies standing at the right or left side of the desk. These are not rules, but just to share how a native english speaker may take the phrase. But you are right, in a general way, the sentences are the same, because implications are not facts.

Yes, both phrases could be understood as The boy is standing next to the desk. In everyday conversation, ‘Beside’ is not as common as ‘next to’ or ‘at’ though.