No, Nvidia does not produce video cards themselves. They make the "guts" of the video cards, which they sell to other companies, who use them to make the video cards that they sell you.
But all these cards are referred to by the model of the Nvidia guts in them of course. Though a gtx 680 from one company may be clocked up higher than a gtx 680 from another company. And the amount of memory installed on the two cards may differ. And the number and type of interface connections may differ. But they are both gtx 680s.
The numbers are just Nvidia's weird little naming system for their video card guts. The gtx 6xx cards are the latest generation. Last year's cards were the gtx 5xx bunch, and before that you had the gtx 4xx cards.
The last 2 digits give you an idea of whether this is a budget, mid range, or high end card. Your gtx 690 is a damn high end card. your gtx 680 is not quite so high end. Your 650 is a bit of a cheapie.
Same for 5xx's and the 4xx's. This is why your 650 costs less than your 580.
There is no underlying reason for any of this, this is just how nvidia's been sticking the labels on here lately, the last few years. They may confuse us with a totally different labeling system later on.
The best way to get an idea of how different video cards stack up against each other is to look at benchmark charts on websites like anandtech.com and tomshardwareguide.com
What company makes the card isn't generally so important, except in terms of that company's reputation for quality and how difficult they are about rebates and so on. EVGA is considered pretty good. Actually I've had pretty good luck with most of them, even the cheap ones.
Main thing to look at is the model number of the nvidia guts, the clock speeds it comes with, how much memory it has, and what the outputs are and what the power reqs are. And how much it costs.