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).
Meaning is that abstract, fuzzy thing in your head that a word or a phrase represents. It includes what the word denotes and what the word connotes, but it also carries associations in memory, the context in which it occurs at the present and in which it had occurred in the past, class , regionality, ethnicity -- a whole panoply of things that, in the end, prevent most words from ever meaning precisely the same thing to two different people.
A definition of a word is an explicit statement in other terms that is intended to capture the meaning of the word. In a formal, sense one should be able to replace the word with the contents of its definition, but often the complexity of meaning of an individual word is too great to be captured in a short sentence.
Ordinary language is, at best, a tool that allows us to convey a very good approximation of what we mean to others. (We'll leave the narrowly-defined and deliberately precise professional and technical vocabularies aside for the moment.) Obviously, there isn't going to be a lot of communication going on if we can't reach some sort of agreement on the broad meaning of words. If I use red to talk about a small furry creature that you would call Thursday -- well, that's how wars get started. So we agree to call it a hamster for no good reason other than that we can agree on the word. We can express that broad agreement in a definition, an alternate word or phrase that means approximately the same thing to both of us. Still, the word hamster means something completely different to my sister (who loved her pet dearly and was devasted by its passing) than it does to me (who was annoyed by the racket it made, disgusted by the droppings it left everywhere, and who had to tear the ductwork apart to retrieve the thing after it made its way through the cold air return register), even if we agree on the definition of the word, and therefore the looser sense of the word meaning.
A dictionary is a collection of those alternate words and descriptive phrases, those definitions that we've agreed upon. A very good dictionary may define a word well enough that you begin to get a sense of its meaning, but ultimately the word will mean whatever that abstract, fuzzy thing in your head that it points to tells you it means.
Best Answer
Right and left are variable directions. Right-handed and left-handed are fixed attributes.
Right and left are indications of orientation based on the viewer's current position.
I am left-handed. Whether I am viewed from the front or back, my left hand is always the same. (I think that right-handed people may have a similar experience.) Clothing and things that are based on human anatomy maintain their left-hand/right-hand orientation no matter how you rotate them.
Additionally, certain objects that are dependent on human control are given a handedness, such as cars and boats. The left front tire is the one on the driver's left hand side in front of his position when driving. Even when the driver walks around the car, the left[-hand] front tire is fixed in that spot, even though it may be on the left or right of the driver as he looks at it from various vantage points.
Similarly, the starboard side of the ship is to the captain's right when she is on the bridge, facing the prow. When she is on the prow, facing the bridge, starboard is still on the boat's right, even though it is on the captain's left.
Right-hand screw threads always turn in the same direction. When looking at the axis of the threaded object, turning it clockwise (top moves toward viewer's right hand) the threaded object moves away.
Finally, in the theater, sides are locked in. Stage left is to the actor's left side when he is facing the audience. If he turns his back to the audience, the stage's left-hand side does not shift, even though it is now on the actor's right. Move to your left is not necessarily the same as move stage left. Both the actor and the stage carry their handedness with them and instructions need to be clear which is intended.
(Since all the world's a stage, and actors come and go, I think stage directions will usually prevail.)