I'm completely at sea with magnification, crop, zoom and telephoto

Lenses are described in terms of focal length, and all you really need to know about focal length is that shorter focal lengths give a wide angle view, and longer focal lengths give a very narrow view. That is, a wide angle lens (again, short focal length, like 10mm or 20mm) packs most of what you see before you into the image; a lens with longer focal length (say, 200mm or 400mm) puts a smaller part of the scene before you into the image, and since that part of the scene takes up the whole image, the objects that you can see in it obviously appear larger. So, long lenses make distant objects appear larger.

You're spot on with your understanding of macro lenses. Every lens has a minimum distance at which it can focus; macro lenses can focus closer than other lenses, so they're able to get good shots of small objects that are very close to the camera. The fact that a lens is a macro lens won't help at all with distant objects, but some macro lenses have long focal lengths and are therefore still good at shooting distant objects too.

The term telephoto really indicates a particular kind of lens design that allows the lens to be shorter than it's focal length. Long focal length lenses used for photography are most often telephoto lenses, though, and so telephoto is often used to mean any long focal length lens, i.e. the opposite of "wide angle."

A zoom lens is just a lens that has variable focal length, so that you can change the angle of view. There are wide angle zooms that go from, say, 8mm to 15mm; mid-range zooms that cover a relatively wide 24mm to relatively long 70mm or 105mm; and telephoto zooms that cover distances like 70mm to 200mm, or maybe 100mm to 400mm. The fact that a lens is a zoom doesn't necessarily mean that it has a long focal length, but the long lenses that most people carry are more likely than not to be zoom lenses.

Lenses that have a single, fixed focal length are called prime lenses. Prime lenses have fewer optical variables, so they can be simpler, cheaper, and often sharper, but they lack the convenience of zooms.

if I am shooting something which is very distant and I want to make it both larger and clearer, what kind of of zoom/telephoto/macro lens would I require?

You'll need a lens with long focal length to make distant objects larger in your photo.

Clarity is a bit more complicated. If the photo is unclear because the atmosphere is hazy, there's not much that a lens can do to change that. But the lens does impact clarity in other ways. Some lenses produce sharper images than others because they have better optics.

If the objects in the photo move relative to the camera while you're taking the photo, you're going to get a blurred image. Long lenses are particularly sensitive to motion blur. Two lens features can help: large aperture, and image stabilization. A large aperture is able to gather more light, and that reduces the time needed to take the photo, so there's less time for camera or subject to move. Image stabilization is a feature that moves elements inside the lens to compensate for movement of the camera, which also gives you sharper images.

So, to make a distant object larger and clearer, you'll want a long lens with the best combination of optics, large aperture, and image stabilization that fits your budget.

The information above all applies to interchangeable lens cameras like DSLRs and mirrorless cameras. If you're looking at cameras that describe lenses like "18x zoom" or something like that, it's most likely a camera with a lens that can't be swapped for something else. The ideas above still apply, but the terminology is a bit different. Larger numbers, like "24x", indicate a longer focal length than smaller ones like "12x". You generally won't get any indication of aperture. Look specifically for optical zoom capability -- digital zoom just makes the pixels bigger, which will make the image seem less clear, not more.