Learn English – Difference between “funny” and “strange”/”weird”

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).

Mostly conjecture and original research:

A parcel has the modern connotation of being sent by mail, and you normally never hear of the noun used to describe anything else (though you may sometimes hear it in verb form, meaning "to deliver in regular, divided amounts"). The word originated from the Old French parcelle meaning "a small piece or part".

A package also generally has the same connotation. The word evolved from "pack" which has its roots in Old German, to basically mean "the product of packing" similar to the etymology of "baggage". While a package is often sent by mail, you could hear of a "package" being stored, or of a "gift-wrapped package" being delivered in person.

A packet is a newer word, with forms first appearing in the 1500s (vs the 1200-1300s) in Middle French (pacquet). The word originally meant "bundle", but now typically has one of the following connotations:

• A small envelope containing spices, grain, seed, or similar material.
• A collection of papers or other information, often bound, as in the written material for a presentation.
• A chunk of data sent over a network.