Neither of these 2 connectors. It that link the black one is a 16 pin IDC connector designed for flat cables and you will ntice a polarising key half way down the side… The blue one is a high density sub D type commonly called a “VGA connector” but properly designated as DE15, actually 15 pins in a 9 pin housing (hence high density description) the orientation keying being provided by the “D” shape.
A brouse on Element 14 or RS Components web sites would probably find your connector, note the polarising points are on the ends.
Are those pins spring mounted? If so, it is for flexible strip, not ribbon. A strip has exposed pads that press against the pins using a clip. If so it would be called a Male-on-Board connector. # Male-on-Board
Do you have the cable that came out of it? Is there a manufacturer mark or name on the side? Have you measured the pin spacing?
The 20-pin is just a type example. The data sheet lists 10-pin to 50-pin, including 16-pin. So if it’s the right one your part number would be CI1116SD0010-NH. It’s very unlikely you would find a cable already made up, other than as a manufacturer’s spare part. However, if it is a IDC connector on standard spacing then it is possible to make it up from components using a small vice and some careful manipulation.
Not rocket science. You could measure it. The pitch is the distance between pin centres. Or possibly an easier way is from one side (left or right) of one pin to the same side of an adjacent pin.
You could be right unless going back to the manufacturer is an option. What happened to the original cable. Someone get a bit rough?
That seems strange. I find it hard to believe a company would produce a product using a connector with no information provided or indeed an adaptor cable to some sort of “standard” such as your VGA 15 pin D unit. The video is obviously VGA as that is what is marked on the board.
Personally I would push the NAS supplier as you would rightly expect to be able to use this thing “out of the box” and you would expect to be able to plug a VGA monitor into it without looking for an obscure adaptor of some description.
Best of luck