The Manage Website Data button is for displaying a list of cookies on your computer, for Safari. Other browsers will have their own cookie stash. Technically, they are cache data of sorts, but they're still all just cookies.
Yes, remove all will remove all cookies - that can be. A cookie that won't clear from the list typically means it's active. That is, it's being held open by an iCloud process, or a web site you have open.
And the web site doesn't have to have the name of the cookie to dump it on your computer. It can be from a site you have open, but the cookie name is seemingly meaningless. Many sites also dump multiple cookies on your computer. Adobe has three on my Mac. And those are just the obvious ones with Adobe in the name. Others may come from a site that dumps cookies for the ad content you see from yet another server that display through the site you're on. Meaning, a single site could easily dump 3, 7, or more cookies onto your computer.
But cookies are harmless. They aren't apps, so they can't do anything on their own. They store simple data, like login passwords, shopping cart data (like for Amazon), region choices from the first time you visit a site that asks what country you're in so it doesn't ask every time you visit that site. The only annoying one is tracking cookies that tell a site your browsing habits. But Safari blocks most of this kind of tracking. It's the type of thing where you look at, say, an umbrella at one merchant's site, then that same umbrella appears on entirely unrelated sites that also sell that item, or similar ones. In other words, they're intrusively nosy, but that's about all.
On top of all of that, when you remove all cookies, they will multiply like bunnies again almost immediately. They really aren't worth much of anyone's time to pay attention to them. And, oh! If you select the check box in Safari's prefs to block all cookies, you'll find the internet very difficult to use. Many sites won't even load unless you allow them to store cookies.
