At least you were taught this.
I'm only trying to figure it out by myself.
Pixel/inch is printing related. Digital images don't have an inch or "reality" size stored, they only have their pixel size. Only with the software you use for printing them, you define a "real" size, and then (on the print) the picture quality becomes mesurable in ppi. So even an image with low pixel count can have a very good ppi quality if you print it small enough.
Example:
IIRC normal photos have a quality around 200 ppi (for print it's called dpi). If you want a print of exactly this quality, at size 3.5 x 5" (9x13cm, a common german size) you need a digital source image of 700x1000 pixels.
If you would print the same image at size 7 x 10" the print quality is reduced to 100 ppi.
Some software/printers could try to increase the ppi/dpi with there own interlacing procedure, but the print won't contain more information. Only a nicer looking bluring instead of graininess.
For images viewed on monitors, the originating ppi is based on the monitor quality (LED/inch or something). And the smallest point, a monitor is able to display at a choosen resolution, is illuminated with the color stored in one image pixel (if displayed at 100% size).
But an image floating around in virtual reality just doesn't have a fixed inch size. You'll notice that, if you should ever start working with a ruler on the monitor and try to get the same results on a different working station with the same file.
I'm just guessing, but the interlacing you deem as a better quality of jpg files will be the compressing method of this format. That means a 640x480 image is reduced in file size, because jpg stores the original information of (ie) only 320x240 pixels and interlaces them back to 640x480 pixels everytime the image is displayed. - In the end that means, to reduce the file size the image loses quality (original pixel informations).
But if you enlarge a jpg it'll still become grainy like any other digital image, and you'll also enlarge the artefacts (sideeffect of the jpg interlacing) that you'll have to remove.
Bmp is a quality lossless format like tga, that's why the file size is so big. It always stores the original data for every pixel of it's resolution. But that doesn't mean that it's in any way more grainy than a jpg.
Damn that's complicated stuff.
I just want to say there's no way, a compressing format makes an image looking nicer for me, than a lossless format.
Of course, the other way around one can always say a grainy picture looks better if it's blured, but that is part of editing the image, and not part of bmp/jpg format selection.
EDIT: Just had a second look at Paintshop Pro. Some image formats, especially the unique ones of some editing software store a pixel/inch value in the file, but that remains somekind of "quick 1:1 print size" help, and doesn't bind the image forever to this ppi quality. Printing the the picture not in this defined 1:1 size would already change the ppi quality, as the pixel numbers stay the same and the inches change.
EDIT2: I somewhat got your point now.
Attached are screenshots of an image, saved quality lossless and also as jpg with 50% compression. - You can achieve somekind of bluring effect that way, but also the quality loss is remarkable. I wouldn't recommend it.
EDIT3: @Lotus
You could attach your original screenshot zipped to this topic, telling us which part of it you want as overview picture. Everyone who likes could do his best on editing it, and attach the result with some explanations of the work.