Learn English – difference between kind and type

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.

The meanings of jargon terms often have essentially nothing to do with the meanings of the English words they're made from. Nowhere is this more the case than in mathematics.

I would use whichever term seems better established—regardless of whether it sounds artificial to native English speakers who aren't mathematicians—so as to give the reader the best possible chance to figure out what I'm talking about.

Updated: I should just answer your question. To my ear, there is a verb filter, and a count noun filter. There is also a non-count noun filtration. (You can count coffee filters, but the filtration of water through coffee grounds isn't something you can count.) So already the mathematical use of filtration as a count noun ("a filtration") differs from the everyday use.

I am pretty sure I never heard the verb filtrate used in everyday English until I started searching for such uses just now. A Google search for filtrated hits mainly dictionary sites. At the moment, the first non-dictionary hit is a link to this question! I can confirm that to my ear, it's hardly a word, and it sounds weird and artificial. Filtered sounds much nicer to me. It is an actual common, everyday word (and, correspondingly, gets hundreds of times as many Google hits).