What’s the difference between a macro lens and a telephoto lens?

There is no direct relationship between Telephoto focal lengths and Macro capability.

Macro lenses allow closer focusing than most lenses. By allowing you to get the subject closer to the camera, it allows you to increase the size of the subject in your photo. Macro capability is measured in terms of Maximum Magnification (MM) that is only indirectly related to focal length. Magnification is expressed as the ratio between the actual size of the subject and the size of the subject's image that is projected onto the film/sensor. A 1:1 Macro lens, which has an MM of 1.0x or 100%, means if the subject is 15mm tall, the lens can get close enough to project a properly focused image of the subject on the focal plane that is 15mm tall. A 1:2 lens would have an MM of 0.5x or 50% and would project an image 7.5mm tall of the 15mm subject. This is because if both lenses are the same focal length the 1:2 lens would require twice the distance to properly focus on the 15mm subject.

Most Telephoto lenses are designed to focus on distant subjects, not to reproduce nearer subjects at high magnifications. A 600mm lens will do very well at taking a 6 foot tall human at very large distance (a little over 400 feet) and filling the 36mm tall sensor frame (full frame is 36mm x 24mm) in portrait orientation. I've never seen a 600mm lens that can get close enough to a 36mm subject to fill the same frame and properly focus on it. By the time you are close enough to the subject, you are inside the lens' Minimum Focus Distance (MFD) by several yards/meters. Most telephoto lenses have very large MFD and thus small MM numbers. That is what a Macro lens is designed to do: by reducing the MFD you can focus on a much closer object and get a higher MM.

There are some telephoto zoom lenses on the market, usually in the 70-300mm range, that claim to be Macro capable. But if you examine the specifications of such lenses, you see that at best they are 1:3 in terms of magnification. They can only focus close enough to project a 15mm image of a 45mm subject. That gives them an MM of .33x or 33%. While it is theoretically possible to design a telephoto zoom lens with 1:1 Macro capability, it is not practical. Most true Macro lenses have a fixed focal length designation that allows them to be simpler, cheaper than a comparable zoom lens would be, and produce better image quality at closer subject distances.

There are some fixed focal length prime lenses that fall into the Telephoto range in terms of focal length and also are capable of close enough focus to be Macro lenses. But a lens doesn't have to be a telephoto lens to have Macro capability and there are many Macro lenses that have shorter-than-telephoto focal lengths.