Does the Peel connection with Amazon understand if a customer is the same in both platforms?

Unfortunately this isn't the case - Amazon doesn't share this detail of information with any other companies so this data isn't accessible.

Amazon's unique identifier for each customer is hidden to everyone, unlike Shopify, so this means that the same customer would be treated as two separate first time customers. Even if a customer uses the same exact information (email, phone number, address) on Shopify and Amazon, there isn't a way to tie the two together.

You are able to segment between Amazon customers and Shopify customers to compare them outright, it is just the individual customer account information that doesn't sync.