From what I know they have a fixed focal length and provides a great depth of field. If they both does the same job, then why are they called as Prime and Macro?

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Canon has one specialty macro called the MP-E 65mm.  Whereas most macro lenses can also be used as normal lenses (while you can focus on a very close subject, you can also focus on subjects all the way out to infinity) the MP-E 65mm can ONLY focus very very close.  It's closest focus distance is 5:1 ratio (object is 5x larger on the sensor then in real life) and the farthest you can be is a 1:1 ratio.   It's almost as if you're attaching a microscope to your camera (not quite, but that's the general idea) because you can photograph very tiny things and make them appear large.

Field-of-view (also known as FOV) ; 45mm. 43.6. 29.9 ; 50mm. 39.6. 27.0 ; 55mm. 36.2. 24.6 ; 60mm. 33.4. 22.6.

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Zoom lenses that boast a macro feature enable you to get in a little bit closer to your subject but don't have true macro features.

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Canon's macro lenses are very good, though one or two of them aren't particularly easy to use. The EF-S 60mm macro is an old but still widely admired lens that isn't very expensive. I'm somewhat familiar with it because my wife has one, and she's gotten good results with it.

For a prime lens, the close focusing distance is usually even better... often 1:2 scale and even 1:1 scale.  At a 1:1 scale the image on the sensor would be as large as the object in real life.  The sensor on a Canon EOS DSLR with an APS-C size sensor (camera's that can use EF-S lenses) is roughly 23mm wide by about 15mm tall (using liberally rounded values).  Since the penny has a diamter of 19mm that means that the image on the sensor would be so large that the penny would barely fit in the frame in the wide direction and would actually be slightly cropped off in the narrow direction -- that's pretty close.

The normal reason for selecting a 'macro' lens is to do close-up photography (even though the lens can also be used for subjects which aren't close).

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I used to own the EF-S 60mm f/2.8 Macro USM and can vouch for the fact that it's an extremely sharp lens.  I no longer own it (I no longer have a camera body that would use it -- I now mostly use full-frame cameras) but I've have no hesitation in recommending it.

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I'm planning to buy a new lens, and is completely confused on which one to buy, a EF-S60mm f/2.8 Macro USM or EF85mm f/1.8 USM Prime.

You need to decide on what you want to do with the lens.  Although a macro lens can be used in other applications it is not the best choice.  A macro lens needs to be used as a macro lens.

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Some zoom lenses indicate that they are also 'macro' lenses... usually that means they can get close enough to a subject to allow capture at about 1:4 or even 1:3 scale.  That is a comparison of the size of the image on the actual imaging sensor as compared to it's size in real life.   A penny has a diameter of 19mm... if you photographed a penny at 1:3 scale it would mean the size on the image sensor is 1/3rd of 19mm or about 6.3mm

Everything Ernie said in his reply is accurate, but one point that he didn't quite make is that the main reason for choosing a macro lens is so that you can take pictures up close to the subject. A macro lens is usually not a zoom lens, because you'd probably always use it at its telephoto end if it were, and good optical quality is a bit easier to achieve in a prime. Some zoom lenses claim a macro capability, but that's usually just a side effect of the lens's ability to change focal lengths.

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The major differences between a macro prime lens and a conventional prime is the magnification factor of true macro is typically 1:2 or 1:1.  It's also my understanding that a true macro lens has a flatter plane of focus than a conventional prime.  If I were to take a photo of a wall mural with a macro lens, the mural will be sharp from left to right, edge to edge.  But, with a conventional lens, the focus may soften near the edge of the frame, because the "plane of focus" is more cylindrical, compared to a macro prime, which has a flatter plane of focus, much like the wall.I'm not sure what you mean by "great depth of field" in this context.  Do you mean narrow, or deep?  When a macro lens is used like a conventional lens to take a portrait, its' depth of field will be comparable to conventional prime.  But, all of that changes dramtically at macro focusing distances, where the depth of field can become as small as 1/8 of a inch, or smaller.  This extremely narrow depth of field is a natural byproduct of focusing at such short distances.  People use macro rails to change the distance to the subject, to take a series of photos for image stacking.  This is where having a flatter plane of focus has an advantage.If you are planning to buy a new lens, and are seeking advice, then tell us how you plan to use the new lens.  Different lenses can be used for different shooting scenarios.  A macro lens gives you the ability focus on subjects that are extremely close to the lens.  There is little significant difference between between images shots with a macro prime and a conventional prime under typical shooting scenarios.

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The physical construction of a macro lens is different than a 'normal' or zoom lens.  The front element is often smaller and flatter and deeply recessed. Also they are corrected for optical aberrations when focused very close.

For a 'Prime' lens, the focal length is fixed (e.g. if it's a 50mm lens then it's 50mm... there's no zooming tighter or wider).

Simple answer, a prime lens can not change its focal length.  True macro lenses offer a magnification factor of 1.0x or 1:1 at its closest focus setting. They are usually prime lenses.

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From what I know they have a fixed focal length and provides a great depth of field. If they both does the same job, then why are they called as Prime and Macro?

For a 'Macro' lens (and macro lenses can be either zoom or prime) the lens is designed to allow a closer focusing distance than most lenses.

I'm planning to buy a new lens, and is completely confused on which one to buy, a EF-S60mm f/2.8 Macro USM or EF85mm f/1.8 USM Prime.

Another generalization about macro lenses is the tend to have optics that resolve very fine detail which is a bit cleaner than most lenses.

Macros as stated above are for taking closeups of tiny things. True macros are all primes. I don't know of any true 1:1 macro that is a zoom lens, but I believe it is only because the way you use a macro there is no strong reason to zoom. To get full magnification you are shooting from between a few inches away from the subject with a 50mm macro lens to maybe 2-3 feet away from the subject using a 180mm macro lens, so why would you really want to zoom?