The most obvious diff is that the macro lens will focus much closer.
It takes special optical design for a lens to be able to focus very close... it's optimized for the purpose, called a "flat field" design.
In order to focus all the way from infinity to 1:1 magnification, a macro lens needs to move it's focusing group a long, long way. In some cases this makes the macro lens considerably slower focusing. In fact most macros are a "long throw" focus, deliberately designed to focus more slowly, emphasizing accuracy of focus over speed of focus.
But it varies... the Canon EF-S 60/2.8 USM is fast focusing, would be hard to distinguish from 50/1.4 or 85/1.8 non-macro lenses. The Canon EF 100/2.8 USM and 100/2.8L IS USM macro lenses are also reasonably fast, a little but not all that much pokier than the non-macro EF 100/2 USM or 135/2L USM. However the Canon 180/3.5L USM Macro is noticeably slower focusing than EF 200/2.8L II or any of the Canon 70-200mm zooms. The EF 180/3.5L is perhaps more specialized as a macro-only lens.
The Canon 50/2.5 Compact Macro uses micro drive, simlar to the EF 50/1.8 II. But both are slower focusing than the EF 50/1.4. Note that the EF 50/2.5 also is a 1:2 lens, not able to do full 1:1 magnification on its own. A matched adapter is needed for that, adding considerably to the cost of the lens.
A macro lens that doesn't use internal floating elements will nearly triple in length going from infinity to 1:1. This can mean balance problems and reduces working distance.
One solution is an IF design, where all focusing is done internally. However, this makes the macro lens much larger and heavier to start with. An IF lens also actually changes focal length as it's focused closer. You don't really notice it in use, but the Canon EF 100/2.8 USM (for example), is actually closer to a true 70mm when focused to maximum magnification. IF design also adds complexity and cost.
So a non-macro lens can be a lot less expensive, faster focusing, and smaller/lighter.
You also can make a non-macro lens focus closer by adding macro extension tubes behind it. In general, though, because the lens isn't a "flat field" design, you'll see some softness in the periphery of the image and might also see some vignetting. And, adding extension tubes physically lengthens the lens, so at higher magnifications you might have little working space between you and the subject.
Finally, the largest aperture available on most macro lenses is f2.8. Often it can be useful or desirable for some types of photography to have even larger apertures available. Portrait photographers, for example, may need to strongly blur down a background to "separate" the subject. Many 50mm lenses are f1.4, up to two full stops faster than macros of the same focal length. Some 85mm enjoy a similar advantage, most are at least one stop or 1-1/3 stops faster. And the 100mm example given is a full stop faster.
This isn't true of all macro lenses. The Tamron SP 60/2.0 Di II offers an f2 aperture, though it's a "crop only" lens. The Zeiss 100/2.0 Makro ZE also offers f2 and is full frame compatible, but is manual focus only.
I just recently bought and am currently experimenting with the Tamron SP 60/2.0, to see if it can replace three lenses in my camera bag (a macro lens and two portrait lenses: 50/1.4 and 85/1.8). It is IF and can do full 1:1 macro, and so far autofocus speed seems adequate (shorter focal length macro lenses can be expected to be faster focusing), but it lacks some of the features found on other macro lenses. It can't be fitted with a tripod ring (but is small enough it might not be all that helpful anyway). It doesn't have a focus limiter, which some macro lenses do, that's another method of helping the lenses focus more quickly. And, as mentioned already, it's crop only, so I'll only be using it on my 7Ds.
If you are mainly interested in shooting macro, get a macro lens. Some can serve dual purpose fairly well, such as for an occasional portrait or any other, typical use of a short telephoto.
If you are mainly interested in non-macro uses of the lens, get a non-macro lens. Then if you occasionally want to do macro, simply get a decent set of macro extesnsion tubes to use on it (the Kenko set is good, comparable to the Canon, which are only sold individually and work out to be quite a bit more expensive than the set of three). Cheaper than the Kenko, there are Opteka and Zeikos macro extension tubesets too... they are a bit more plasticky, so I might think twice before using them with heavier gear. But macro extension tubes have no optics in them that might degrade images and are easy to use. Note: the Zeikos tubes are sold under many other brand names, including Bower, Vivitar, ProOptic (Adorama house brand) and more. The Zeikos also come in two versions: a model with metal bayonet mounts and an even cheaper version with plastic bayonet mounts. I'm not sure I'd trust the latter with anything more than a very lightweight lens.
Personally I usually make a distinction between macro and portrait lenses, too, in that macro lenses are able to resolve a great deal of fine detail, which isn't always a desirable thing for portraiture. Most of us aren't photographing 17 year old models with perfect skin, fresh from a $200 an hour makeup session... A macro lens might capture too much fine detail for portraits of "real" people.