On the same APS-C camera the 18-135mm zoom set at 28mm will give the same Field of View (FoV) as the 28mm lens will. At 18mm the zoom lens will be wider than the 28mm prime lens.
It is when one starts comparing different focal length lenses on cameras with different format sizes (sensor or film sizes) that things get a little confusing. Assuming the lens in question throws a large enough image circle to cover the format in question then the larger the format is the wider the FoV will be for a lens of a specific focal length. But some lenses only provide an image circle large enough to cover smaller formats (sensors/film).
In general lens manufacturers measure the FoV of lenses when those lenses are mounted on a camera for which the lens is designed. They then list what type of view (ultra wide angle, wide angle, normal, telephoto, etc.) each lens gives based on the FoV given for the lens on the camera with which it is measured. The description is based on the field of view of the resulting image when each lens is used with a specific format size.
In the case of Canon the EF-S series of lenses are measured on APS-C cameras with a 1.6X crop factor compared to FF cameras. Those sensors are roughly 22.3x14.9mm in size. The EF series of lenses are measured on full frame (FF) cameras with sensors that measure about 36x24mm in size. An EF-S lens on a 1.6X crop body at 18mm gives almost the same FoV as an EF lens at 28mm on a FF body. For this reason the 28mm lens that is designed for a FF camera, but can also be used on a smaller APS-C cameras, is listed as a wide angle lens because it gives a wide angle FoV when mounted on the FF type of camera for which it is designed. The 18-135mm lens when used on an APS-C camera gives fields of view ranging from wide angle (18mm) to telephoto (135mm). An 18mm lens that could be used on a FF camera would give a much wider FoV than an 18mm lens mounted on an APS-C camera. For that reason 18mm lenses usable on a FF camera would be labeled "ultra wide angle."
But not everything is about focal length and Field of View (FoV) when comparing a zoom lens such as the EF 18-135mm f/3.5-5.6 to a prime lens such as the EF 28mm f/1.8.
When the 18-135mm zoom lens is set to 28mm and used on the same camera as the 28mm prime lens the FoV will be pretty much the same. What will be different is the maximum aperture of each lens, the overall image quality of each lens, the size and weight of each lens, the number and types of cameras with which each lens can be used, and the price of each lens.
In a comparison of the two lenses given as an example above, the 28mm prime lens at f/1.8 will let in more than four times as much light as the zoom lens at f/4. The 18-135 is a variable aperture zoom lens. It can only open to f/3.5 from between 18-23mm. From between 24-34mm the maximum aperture is f/4.0, from 35-49mm max aperture is f/4.5, from 50-75mm it is f/5, and from 76-135mm it is f/5.6.
There are several advantages of a wider aperture lens. Here's what Brian lists in his review of the EF 18-135mm f/3.5-5.6 IS USM at The-Digital-Picture:
Allowing more light to reach the sensor permits freezing action and handholding the camera in lower light levels and can also permit use of lower (less noisy) ISO settings. In addition to allowing more light to reach the sensor, increasing the opening permits a stronger, subject-isolating background blur (at equivalent focal lengths). Lenses with an opening to at least a specific aperture (usually f/2.8) enable the higher precision AF capabilities (most often the center AF point) in some cameras and present a brighter viewfinder image. Another benefit, especially when shooting in Manual exposure mode, is that constant max aperture lenses permit that max aperture to be set and remain constant regardless of the focal length selected.
And from the same review the advantages of lenses with narrower maximum apertures:
The advantages to a narrow aperture, because the size of the lens
elements can be reduced significantly in size, include smaller size,
lighter weight and lower cost. Those are three things that we all can
In general prime lenses also have better optical image quality because the design can be optimized for the single focal length of the lens. The multiple focal lengths of a zoom lens means compromises must be made to allow it to be used over a wider range of focal lengths. The wider the range between the widest (shortest) and longest focal lengths, the more the design must be compromised.
There are a few very good zoom lenses that have optical quality that approach or equal the optical quality of their prime lens counterparts. The Canon EF 24-70mm f/2.8 L II when set to 50mm has image quality every bit as good as the EF 50mm f/1.8 STM. The zoom lens currently sells for around $2000 in the U.S. while the prime goes for around $100. But the prime can still open up to f/1.8 while the zoom can't let in more light than f/2.8. The zoom also weighs about 28.4 ounces compared to the 5.6 oz. prime lens.