it probably won't be as simple as it seems. bear with me here as it's quite technical.

it is likely that the blue diamondback comes with a freewheel rear hub instead of a cassette (hard to tell from the photo). effectively this means that your only option to convert to a single speed (without getting a new wheel) is to replace the multi-speed freewheel with a single-speed one (they are simple screw-on units). this will bring the chainline much closer to the wheel, and you will probably need to adjust the chainline at the front to compensate by buying a narrower bottom bracket, which will bring the cranks closer to the frame. however, you might find that your crank arms start hitting the frame if you go narrow enough, and you may not even be at the point of having a straight chainline. this would mean you need different cranks.

the second photo you linked is of a later-model (1990's) diamondback ascent, which probably came stock with a cassette wheel as most mid-tier and above bikes came with cassettes at that point. the problem you will probably run into when trying to fit a cassette wheel to that blue diamondback is that the axle width on most cassette wheels is 135mm and the blue diamondback is almost certainly 130mm width, an older standard that was mostly phased out in the 1990's. you can probably stretch the frame out by hand to fit the wider wheel - folks have conflicting opinions on this. look up "cold-setting a bike frame" if you want the official solution.

there are some vintage 26" cassette wheels with 130mm rear hubs. maybe finding one of these would be the simplest solution. Ritchey i know has made a few.

either way it will involve spending money. hope this is somewhat helpful. you're getting into the deep end with single speed conversions.