How can stockings (not pantyhose) be worn casually rather than fashionably?

By doing so.

If you don’t want to wear stockings to be fashionable, the only difference is in intent. So wear them with different intent.

Since it’s relevant I’ll relate a recent apparel decision I’ve made:

I hate pantyhose and tights. I also never wear pants, so (in winter mainly) tights are necessary. Pantyhose not so much, they’re too thin to do much against cold weather, at least I don’t have to bother with them as much. Still, the weather going cold always heralds the frustrations of these damn things.

So this year I decided to explore my options. I tried stay-ups like the ones you linked to. Even more frustrating than tights, as all the ones I tried lost their staying power long before the day was over. Over knee stockings like the ones pictured in another answer were tried too, but I’ve got a lot of short skirts (at my grandmother’s insistence, a longer story), and those’ll make for freezing thighs when the snow flies.

My last option was garter belts and stockings. At first I didn’t seriously consider this, most of the stockings that go with garter belts are a lot like the stay-ups you linked to with broad bands of lace. Don’t get me wrong, I like some lace. But not that much and not with every outfit. And with shallow searching I only found stockings up to 20 denier, still quite thin. But when I ruled out the other options, I searched more assiduously, and found thicker stockings in more styles, so back on the option board.

I’ve now tried out and purchased various garter belts and stockings that work as I want, and when the weather turns cold I’ll be wearing them. Not to be fashionable, not to make a statement, not to be sexy, but for everyday comfort. That’ll count as casual, because that’s the intention behind it.