An expired subscription is one for which the valid dates of the subscription have passed. Either there was a set term on the subscription when the customer signed up which has passed, or the customer has logged into his/her account and entered an expiration date in order to cancel (if allow suspending option is active in Subscriptions / Preferences). Alternatively, the customer called/emailed and someone entered an expiration date on the customer's subscription record in the Order Management System. An expired subscription has no future order date.
A Suspended subscription has had some sort of problem with processing the subscription, and the maximum number of retry attempts has been reached (Subscriptions / Preferences/Maximum Retries). The problem could be the customer's expired card and lack of action to return and update the card, or a problem with the actual product for the subscription (i.e. out of inventory), etc. But after the maximum number of retries has been reached, the subscription becomes suspended.