My question is if a lens like a Tamron 90mm 2.8 could be used also for portrait. If not, why ? What are the difference between a specific portrait lens (like any 85mm 1.4) and a 90mm 2.8 ? Only the different aperture ?
Macro and portrait lenses are generally designed to do two different things that require different design characteristics.
Macro lenses are designed to focus at very close distances and they typically render a fairly flat field of focus. There are a few very specialized macro lenses that can only focus at the very close focus distances required by macro photography and would not be suitable for other types of photography. Most macro lenses, however, can also double as general purpose lenses. These can be used to focus at more typical focus distances and many photographers have a 90-100mm macro lens that they also use for portraits.
Other lenses specifically designed for portraiture often have a more spherical shape to their field of focus. The Canon EF 85mm f/1.2 L II is one such lens. They typically can not focus anywhere near as close as a macro lens can. There are reasons some photographers prefer to shoot portraits with a lens that has field curvature.
The field curvature that is a characteristic of many lenses purposely designed for portraiture would make most everything except the center of the frame extremely blurry due to the very shallow depth of field if used at the extremely close distances involved in macro photography.
On the other hand, the narrower maximum aperture of most macro lenses remove the option of wide aperture bokeh and shallow depth of field when compared to many prime lenses designed particularly for portraiture. The correcting elements needed to render a flat field of focus also tend to make out of focus blur, often called bokeh, a bit harsh. Macro lenses are also generally designed to be sharpest at close focus distances. Sometimes, but not always, they are also very sharp at longer focus distances.
Such macro lenses with very sharp performance across the frame, even at longer than minimum focus distances, are excellent choices if your goal is to make the highest quality photos you possibly can of flat test charts. They're not always the best choice to get the characteristics many portraitists are after.
A perfect example of why a Macro lens is not always a good idea for portraits:
Macro lenses are close focusing lenses. While most macro lenses can be used for photography that does not require close focusing, they are specifically designed for this ability. A typical 85mm f1.4 will not be designed to focus at close distances. The primary design of a macro lens is to be good for very close up work, whereas the primary design goal for a portrait lens is different. A macro lens might not be designed for good bokeh, for example, but it is typically very important in portrait lenses.
Typically a true macro lens will allow a magnification of 1:1 ( meaning the image size on the sensor or film will match the actual size of the object ), whereas a portrait lens has no need for such extreme magnification.
The Tamron 90mm f2.8 ( and long ago the f2.5 ) is perhaps the best known of macro lenses and have always been regarded as fine lenses.
It is much easier to objectively classify a lens as a "macro lens" than a "portrait lens" and that's probably why few or no lenses feature any references to portraiture in their branding and/or designation. "Macro" most often means that the lens can get to 1:1 magnification - that is it will project an object as big as it really is - for example on an APS-C sensor (typically around 24 x 16 mm) you can fill the whole frame's height with a coin that's 16 mm in diameter.
Note - what others said that "a lens is a macro lens if it can focus from close distances" is somewhat wrong. Magnification is a function of focal length and object distance - so for example a Nikon AF-S DX 35 f/1.8 G and a Nikon 105 f/2.8 VR G can both focus as close to about 0.3 m, but whereas the 105 has 1:1 magnification, the 35 only goes to about 1:6 (about 0.16). Then there's the AF Micro-Nikkor 200mm f/4D ED-IF that hits 1:1 at 0.5 m.
There's also a few special macro lenses like the Canon MP-E 65mm 1-5x Macro - which not only does a 1:1, but it can do 5:1.
Some manufacturers brand some lenses as "macro" when they can only get to 1:2 or 1:3 magnification, but that's rather a marketing trick to fool not very knowledgeable people, usually beginners, into buying a lens like a 18-200 or 18-300.
Following on from Michael and Steven..... I think macro lenses have a different (fine) focus ring mechanism, to achieve absolute accuracy when dealing with a macro shot and the very small depth of field that is typical at the distances normally encountered with this type of shot. The fine ring is slightly slower in achieving focus vs a coarse pitch focus ring, the reason is simply because you have more thread to wind on the screw!
This is the reason why some macro lenses have a range limit switch, a feature also found on some high end telephoto lenses.
You can use a macro lens for portraits, although I don't shoot people often, my macro gives excellent results, but it is my most expensive lens..... With that being said, my cheapest lens also gives very good results! Even a telephoto lens (normally sold as/for wildlife) need not be used specifically for that reason, my tele lens gets used for everything but macro! It takes some nice landscape images, the effect of field flattening is quite nice. Finally, a wide angle lens, normally marketed for landscapes, takes good pictures of cars and aircraft in a museum.
Macro lenses also do not need to be high speed (large aperture). In fact, when shooting macro, you want a smaller aperture because the depth of field narrows as the focusing distance decreases.
The longer the focal length of the lenses, the smaller the aperture you will need, particularly if you are photographing a three-dimensional object (such as a flower or toy car, for example) and you want the entire object to be in focus.
That is why you often will see macro lenses in the 50-60mm range and 80-90mm range. Ideally, you own both lenses and select the one that works best for the situation.
The goal of the lens maker is to deliver a faithful image. The facts are: this has never been achieved. All lenses have residual aberrations that were not corrected by the lens design. There are seven major aberrations and these are mitigated by clever use of materials with different densities. Some of the lens elements have positive power (convex), some negative (concave), some cemented together, and some air-spaced. The lens maker optimizes a general purpose lens to be most free of aberrations for subjects at infinity ( ∞ ). The macro lens is optimized to image at close distances and achieves “unity” (life-size). Additionally the macro is attuned to image objects that are flat or nearly flat. The portrait lens is optimized to moderate aberrations when tasked to image near-by subjects.