Subscription implies a service that is paid for on a regular basis. Membership may be paid for, but that is not implied.
I could be a member of the Zooey Deschanel fan club for free, but subscribe to the monthly Zooey Deschanel magazine for $20 a year, for example. A man can dream...
Also, one can be described as a member of organisations that actually pay you, like the armed forces or emergency services.
Members of a subscription system are generally referred to as subscribers, but this is context sensitive. Your friend could simply refer to them as customers, as that's the usual word for someone paying for goods or services.