I've never seen reference to mate/wire side instead of male/female. Is that a Euro thing?
1. Jack vs plug. The "plug" side is the side that moves. The "jack" side is the side that doesn't move, or moves less. Think of a wall outlet: the "jack" is the outlet and the "plug" is the, well, plug.
2. Male housing vs female housing. The "male" housing goes into the "female" housing. Simple enough (if you don't have to explain it to your six-year-old...).
3. Male terminal vs female terminal. Again, the male goes into the female. But the little conductive pins don't have to (and, often, don't) match the gender of the housing itself. Molex Micro-Fit 3.0 is an excellent connector series that is notorious for having the terminal gender reversed from the housing gender. (And of course, both genders of crimp terminal are available.) This can cause problems if your communication is not perfect, but is still good enough that people actually think they can trust you.
4. Mating view vs wire view. "Mating view" is the view that you'd see if you were sitting on top of the mating connector, just before you got squished. "Cable view" is the view that you'd see if you were riding on the wiring behind the housing. They are mirror images of one another. It can be impossible to tell from a pinout drawing which view it is, even if there is a polarization feature (pin 1 marks are often OK, latches are usually not), so you HAVE to say. The "component view" vs "solder side view" distinction (among other names) is analogous for PCB mount connectors.
All of these issues are but a small part of what makes connectors utterly horrible to deal with. They have wasted more time, money, and effort than you will ever know.
Oh, I'm well aware. I've been making custom cables since high school back when Moses was a baby floating down the river.
If it weren't for all of the confusion, we wouldn't have lovely phrases like "fuck the truck" to help remember which end of the cable goes to the truck.
By hand you can usually only screw it up four or five times (for a cable there are only four ways to make). Sending out orders during New Product Introduction (so nobody knows what they're doing, and the answer to "how did that work last time?" is "in fact, that has never once in the history of human civilization worked") to a cable vendor that engineering (you) recommended be dropped due to quality problems including (but not limited to) "does not read the cable drawing", but management insisted we keep using because "we know how to order from them" (which was awful -- hand delivering parts, dealing with angry dogs in the way, drunken contacts at the vendor, and finding out that not only do their neighbors hate them (no surprise), but they managed to personally (personally!) get on the bad list with their FedEx guy; this is not easy) -- so that is no excuse)... that's how you get to the real pain.
Antennas are the external fertilization of connector sexing.
[1] https://en.wikipedia.org/wiki/Anderson_Powerpole [2] https://www.youtube.com/shorts/rBkcZlOyPsc (NSFW unless you're in the trades)