A customer, by our definition, must be actively paying you for your product or service on a recurring basis.
By this definition:
1) Someone who is fully discounted or credited for their subscription is not a customer.
2) Someone who is on a $0 subscription or trial is not a customer.
3) Someone who has a subscription starting in the future is not a customer.
4) Someone who is paying you through one-off charges rather than a subscription is not a customer.