The word "macro" is thrown around loosely by lens manufacturers... especially third party manufacturers, but OEM do it sometimes too.
There's some difference of opinion about what "macro" itself actually means. Many experienced shooters have concluded that a macro lens should at least do 1:2 magnification (half life size or 0.5X). Less than that is a "close-up" while more than 1:1 (life size or 1.0X) is "micro". Just to confuse the issue, Nikon calls it's macro lenses "Micro Nikkors" and Zeiss spells theirs "Mikro".
But the term has been very loosely used, particularly with third party lenses such as the Kiron 80-200mm you found. But if you look at 80-200 and 70-200 and 70-210mm lenses, you'll find that 1:4 (one fourth life size or 0.25X) is actually pretty good for a zoom... many that are labeled "macro" actually don't come close to that.
Kiron, incidentally, is a somewhat legendary lens maker. The company Kino Precision was started by several former Nikon engineers and designers. At one point, the Kino CEO supposedly stated that "Kiron is 'Nikkor' spelled sideways", referring to the company's intention to compete with the "big boys", producing high quality, innovative products. There have been a number of "cult classic" Kiron lenses, including some "true macro". They also produced a lot of lenses for other manufacturers, most notably Vivitar marketed quite a few under their name (the Kiron lenses in disqguise were identifiable with the serial number prefix system Vvitar used at the time... the Kino Precision made lenses has a 22xxxxxxx serial number).
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If you really want to try photomacrography... get your hands on a Kino Precision Optical 105mm f/2.8 macro lens. They might be labeled as a Kiron, or as a Lester A. Dine, or as a Vivitar, and there are several other brands too. The Vivitar versions may be listed as 100mm, and maybe as f/2.5, but if the serial number starts with 22, it's the right stuff. They run from just under $200 up to $400 or more on eBay. Bide your time, find a low cost lens.
The above is correct. The Kiron prime lenses are especially impressive, although their zooms were pretty darned good, too.
One thing about the 80-200mm... what mount is it in now? If it's Canon FD/FL that would work on your AE-1, any "glassless" adapter to use it on an EOS/EF mount camera would not enable it to focus to infinity. (There are some Ed Mika design adapters that do, but they are specific to certain lenses... only a limited number of primes and only Canon OEM as far as I know.)
"True" macro lenses close focusing ability and magnification potential are only part of the story. In most cases, macro lenses also use "long throw" focus... meaning that the focus mechanism emphasizes precision over speed by requiring more rotation of the focus ring (whether manual or AF) to achieve focus. This can make the lens less useful for non-macro purposes, but is needed for more exact focusing when dealing with extremely shallow depth of field that occurs at higher magnifications.
Many "true macro" lenses also are "flat field" design... this means their optics are designed to offer edge-to-edge sharpness at very close focus distances. "Standard" optics may be designed to achieve edge-to-edge sharpness at 6 or 8 feet (portrait distances)... or even farther, depending upon the lens type. Nowhere near macro distances. This is one of the reasons that a non-macro lens with extension tubes or a reversed lens is often considered not quite as good as a "true macro" lens.
I have one vintage, manual focus macro lens that I occasionally use on my EOS cameras. It's a Tamron SP 90mm f2.5 (1:2 or 0.5X with lens alone) that's also very capable. I paid all of $20 for it at a local 2nd hand store... It's an Adaptall2 interchangeable mount lens that's actually designed to be easily adapted for use on many different systems. I'd used several copies of the Tamron 90mm over the years and was already familiar with the interchangeable mount (rather than adapting a different mount) and knew they were available for EOS. The lens was "like new", with caps, hood and the 1:1 adapter... adn with a Nikon F mount on it. I've also got Adaptall2 mounts for vintage Konica, Olympus and Pentax systems. I ordered a "chipped" EOS/EF Adaptall2 mount from China, where they're still being made, for $40 including shipping.
Here's the Tamron lens mounted on one of my EOS cameras, the lens separate and showing the Adaptall2 for Nikon alongside, and a couple example shots taken with it...
Not bad for a $60 investment, IMO. The lens itself goes to 1:2 magnification, but has a matched adapter making it full 1:1 capable (though I usually just use macro extension tubes instead, which give the same result without any optics and are in my camera bag all the time, anyway).
Lens has a 6-bladed aperture... but at macro magnifications is capable of obliterating backgrounds, as you can see in the shot of the two "fuzzy" poppy buds, above. That's SOOC, not post-processing. The background was an ugly gray garbage can some 8 or 10 feet away.
You should know that the lenses you're considering, the vintage Tamron above, or any other vintage adapted lens will be a bit tricky to work with adapted for use on modern autofocus DSLRs. They'll be strictly manual focus, of course. That's not a problem for macro work, typically (in fact, often manual focus is easier for macro). However, they also are strictly manual aperture, which makes them slower to work with and also dims down the camera viewfinder, in turn making focusing harder. Macro shots often require pretty small apertures in search of adequate depth of field (above were both shot at f11), making for VERY dim viewfinders and difficult manual focus.
A couple things can help. One is to get a "chipped" adapter. These correspond to the electronic contacts in the EOS/EF system. The chip doesn't provide AF or aperture control, of course, but does allow the camera's Focus Confirmation feature to work to some extent (at really small apertures it may slow, struggle and even fail). On many EOS DSLRs it also is possible to use Live View combined with Exposure Simulation (to brighten what you see on the LCD monitor).
That's all fine with stationary macro subjects. But I can tell you it's not ideal with faster moving subjects like bees on flowers! For that bee on the orange poppy, it probably took me 15 minutes or half an hour and 50 or 75 shots to get a half dozen well-focused and, from those, a couple I liked enough to keep. Thankfully, several bees were repeatedly visiting the flowers and busy gathering nectar.
If your primary goal is shooting macro and you can live with the slower process using a strictly manual lens, I'd encourage you to be patient. There are literally millions of excellent, vintage "true" macro lenses out there that are very easily and cheaply bought and adapted for use on EOS cameras, though you rarely see as good a deal as I got on the Tamron 90mm. That Tamron is designed to allow for interchangeable mounts... many other vintage lenses are not, but can easily be adapted for use on EOS anyway. See this website for much more info about adapting old lenses for use on your camera:
http://bobatkins.com/photography/eosfaq/manual_focus_EOS.html. Especially make note of the chart there showing which vintage mounts are practical and easy to adapt, versus those that are difficult and may not be worthwhile (including Canon FD/FL).
Have fun!