If I make a change to a contract, will those changes apply to past submissions?

If my client goes back to their link, will they see the changed contract or what they originally agreed to? 

When you say "their link", meaning, the Edit Link? If so, your client will see the updated contract. Basically, everything will be replaced whether you're making changes in the submission or in the form.

The changes won't appear, of course, in the old email that your client had received before the changes are made.

Thanks

By link, i mean the link i send to my clients to sign their contract. Made some changes, went back to the same link and it showed the updated contract....

Is there a way that clients can see the contract that they signed without those changes?

Unfortunately, that is not possible. A workaround would be to clone the form and then make the changes to the cloned version then use this cloned for your new clients. The old form will remain the same for your old clients.

http://www.jotform.com/help/27-How-to-clone-an-existing-form-from-your-account

Thanks