The Start Date and Expiration Date determine the time period during which a discount can be applied. The duration of a discount depends on what was entered in the Billing Cycle field only.
For example - if a discount is applied to a monthly recurring order on March 30th with the Expiration Date set to March 31st and Billing Cycles set to 2 - the customer will get a discounted price for the next 2 months. The Expiration Date will only prevent customers from using this discount code after March 31st.