What is the point of having a different skill for Persuasion and Deception?

2 skills related to Charisma are Deception and Persuasion. A character could be proficient in any of the two. I know that a Cha (deception) check is made when a character attempts to convince someone else of a lie, while a Cha (Persuasion) check is made when arguments are used to convince someone of something.

To me the important distinction was always: is the arguments you are making based on a truth or a lie?

  • Trying to convince a guard that the king is in danger (a truth) and you need to get in the castle, with the intention of saving him? Persuasion.
  • Trying to convince a guard that the king is in danger (a lie) and you need to get in the castle, with the intention of stealing from the treasures? Deception.

But in the end, you’re still just trying to convince someone. The arguments that you use would be the same whether or not you are lying about them.

I’ve seen people say that Cha (deception) checks involve arguments that are harder to defend/prove. Yet a case where the party is ambushed by ghosts, in the middle of the city, would have a better chance convincing the guards that come asking about the commotion that it was simply a few drunks (Deception), than ghosts (Persuasion).

Why then is there a need for 2 different skills?