I don't see any difference in the way the Spanish has been written

Hola Paris,

The first sentence expressing purpose: "con tal de que me dejes en paz" means "in order to be left alone".

The second sentence expressing condition: "con tal de que me dejes en paz" means "with the condition that you leave me alone" (so, if you leave me alone I will give you my bracelet)

So "con tal de que", depending on the context, can express a purpose or a condition.

I hope this clarified it.

Saludos

Inma