The reason for the division in the law of hiring workers

I don't know this distinction, but if they both agreed that he would work without payment, he doesn't have to pay in both cases. And if they agreed to pay, he certainly has to pay in both cases. So what's the point? Wasn't there a reference to this in their contract? I don't see a difference between the cases. There may be a difference regarding what gives rise to the contract, since the property of a worker is related to the tools he uses or to the commencement of the work. In practice, when hired not to do something, there is no tool of action and no commencement of work, and therefore there is room to say that there must be settled property. But as mentioned, this is a difference that is not specifically related to the payment of wages for the work, but to the scope of the contract. In fact, in these matters, everything is determined by law and not by halacha.