Zen Cart keeps logins in on the admin and storefront side as separate. So you can be logged in to the admin and processing orders, and either not logged in on the storefront or logged in (possibly as another customer) and testing or creating an order.
In WooCommerce, the admin and storefront logins are the same, so if you are logged in as the admin, you are also logged into the storefront using the same account. If you need to view the storefront as a different customer or as someone who is just browsing, you will need to use a different browser.
This is not a huge inconvenience, just something to remember.
When you need to login as a particular customer, either to investigate a problem or help them complete an order, Zen Cart gives you a couple of options: in 1.5.7 and forward, the built-in Place Order capability is provided from Admin > Customers > Customers. If you’re using an older cart, plugins like Master Password can allow you to login as a customer.
In WooCommerce, this capability is provided by plugins such as Use Admin Password. This works well but is subject to the requirement to use two browsers (assuming you are logged in as admin already) as noted above.