Your data is stored through Shopify’s data storage, databases and the general Shopify application. They store your data on a secure server behind a firewall.
Here is a list of cookies that Shopify use:-
_session_id, unique token, sessional, Allows Shopify to store information about your session (referrer, landing page, etc).
_shopify_visit, no data held, Persistent for 30 minutes from the last visit, Used by our website provider’s internal stats tracker to record the number of visits
_shopify_uniq, no data held, expires midnight (relative to the visitor) of the next day, Counts the number of visits to a store by a single customer.
cart, unique token, persistent for 2 weeks, Stores information about the contents of your cart.
_secure_session_id, unique token, sessional
storefront_digest, unique token, indefinite If the shop has a password, this is used to determine if the current visitor has access.