I am building a site that is a hybrid wordpress and shopify store with different pages on different servers. Is there and add on I can use to do this, or a way I can synch the profiles so if they add items to their cart or sign in from one page they will be signed in on both?
Both options do pretty much the same, the first one will give greater flexibility.
In that case you will be able to "put" products from your Shopify store into WP and have a shopping cart and checkout.
As far as I know you can't sync user profiles from your WP to Shopify. I can think at few ways but very painful to integrate.