That sounds a little strange to me. If I have a plumber or an electrician give me an estimate for a job, I don't provide them with a contract stating the work to be done and the terms on which I'm going to pay them. I assume that the professional is going to give me a contract detailing the work s/he is going to do. That's why I hire a professional: I assume the pro knows what s/he is doing.
If you had not provided a contract and you were okay with what the client gave you, there's no harm in signing it. But since you have already given the client a contract, which the client signed, there is no reason for this second contract, particularly if it's incomprehensible and doubly so if the terms don't match what you already agreed to.
I would go back to the client and say something like, "John, we already signed a contract and I've begun work according to the terms we agreed on. I'm a little confused about this second contract. It doesn't match what we already agreed to. What's your thinking here?"