technically -the SYSTEM denotes what machine it fits, the Style is what type of tip the needle has, and the size is how big in diameter the needle has. One item not address is the type of metal and process the needle goes through to harden it. Some processes make metal more brittle, some make it more flexible. And different mixtures of metal (alloys) can react very differently. And now some companies are putting different coatings on the needle after manufacture.
Then there is quality control- some companies have higher tolerances than others, so if the needle is suppose to be .05268 diameter (number pulled off the ceiling) but one company says +-.005 is close enough and another says .0005 is close enough . . .
So there is a lot more going into selection of needle other than System, Style and Size
I have over 150 machines with probable over 15 systems. Now days the vast majority of domestic machines use the same system that Singer started using in the late 1800's (and at the time, they were one of the few US companies using that one).
I have no idea who is actually making the needles that have the Singer brand name on them. I don't know if SVP owns any needle production factories. Sometimes you find many "brands" are made at the same place, but they have different specifications so being made at the same place in no way means they are similar in quality.