Confusion between "birth control" and "contraception" goes way beyond "Catholics". I bet even in your Church (whatever it is) most folks refer to the use of condoms, "the pill", etc as "birth control". That's certainly common usage generally.
By morally equating contraception (which, as I pointed out earlier, happens every single time that people don't engage in intercourse)
Your point is a blatant falsehood. Contraception by definition is something that renders an act of intercourse infertile unnaturally. Not having intercourse may be "birth control", but it is not, and cannot be "contraception".
with abortifacient birth control methods (i.e. anything that murders the already-conceived child at any point prior to birth),
That's one thing the Catholics DON'T do. They're VERY clear on distinguishing "Natural Family Planning" from artificial contraception. There are plenty of things for you to disagree with them about; no need to fabricate anything. And that's what you just did.
Would you say condoms are the moral equivalent of abortafacients? What about low sperm counts? What about tubes being tied? What about vasectomy? Does it matter if any of the above couples have other children?