How do I send responses to a form to a different email address than my first?

I have two forms that should go to two separate emails. 

Hi,

You can do that by following this guide: https://www.jotform.com/help/314-How-to-Properly-Add-Change-and-Test-a-New-Email-Recipient-Address 

To learn more about the settings in the email alert, you can also check this one: https://www.jotform.com/help/30-Explanation-of-Email-Notification-and-Autoresponder-Settings 

Basically you need to open the "Emails" wizard and edit the notification/autoresponder there.

I hope that helps.