パッチ originally came from the Korean 바지. But the English 'patch' (of the software variety) has almost completely overtaken it in usage. And the pictures you found, when narrowing to clothing, feature a patch in the cloth (look around the knee).
I think you can still find it used in Kansai dialect. But everywhere else it's now referred to as 股引 or ステテコ. You'll have better luck searching for those to understand the original intent.
Regarding the English term, I think the fashion term we use where I am at is "leggings". It was mainly seen in exercise clothing, bottoms, yoga pants and such. Nowadays, I can't tell the difference between "stockings" vs "leggings" except the opacity of it (and how many layers are being worn).
Leggings are comfortable skin tight pants with an elastic waist. A good pair of leggings will have pockets!
Stockings are like really long socks. Sometimes they need a garter belt to not fall down. I think thigh highs count as a kind of stocking?
Tights cover the waist and feet. These go from sheer to opaque. Really sheer tights are called pantyhose. There's also really nice fleece lined tights, 10/10 recommend for winter!
Some of these terminology-debates on naming (especially cases like US biscuit vs UK Biscuit) seems to spawn many flame wars in various categories of things, living and non-living e.g. wooden stick (as weapons) naming on different length and thickness.
Unless, it is specific to scientific naming, the layman names and terminologies are preferred to be used for the goal of regional communication understanding. So nowadays I'm usually not too hard up about being pedantic (unless you're in the EU regarding trademarked names e.g. champagne, parmigiano reggiano). Here's one on Prawn and Shrimp as food and here's one on the terminology Shrimp vs Prawn, and the Eggplant-Brinjal-Aubergine. Fun stuff, nonetheless.
