Great original frame and patina to start with! Keep in mind, that bike in your first photos is a girl's frame, and yours is a boy's. And by the chain guard, it is likely they are different models. All that said, the two blues are probably not the same blue. BUT, no matter what, your blue Schwinn can definitely get that luster back to closer to when it was new.
When I first start to clean, I start on the underside of a chain stay, something that won't be seen that easily anyway if I mess up. I start with #0000 steel wool dipped into a 50/50 mix of water and white vinegar. LIGHTLY rub the frame , just brushing it really, with the dampened pad. Probably won't take but a few strokes. Then have an old cotton towel handy to wipe off the area. After it fully dries, 5-10 mins later, you can use a clean cotton rag to buff the area to get the 'hazy film' off, and see what kind of result you have. Then you can proceed from there if it is to your liking. Be especially careful over any stripes or the white paint areas near the head tube, as that is usually applied over the blue, and will come off very easily!
Then after the bike is cleaned, I like to use a car wax, applied with a soft rag and then polished after it dries. My main rule that I use in any form of bike customization applies here,
"Always quit before you think you are done!"
