Welcome to the forum.
First thing to know, is that any Canon 'EF' or 'EF-S' lens will work on your camera. There are also other companies, like Sigma & Tamron, that make lenses to fit your camera.
18-135 or 28-135... What is the main difference between these two?
Focal length. Those numbers are the lens's focal length zoom range. The first one will zoom from 18mm to 135mm. The second one will zoom from 28mm to 135mm.
Focal length will directly relate to the field of view that your camera will see. A shorter focal length will give you a wider view. So the 18-135mm will give you the same wide angle view as your current 18-55mm lens, but it can zoom in much more.
The 28-135mm can only go to 28mm on the short/wide end, so it won't be able to give you as wide of a view as your current lens.
Another thing to know, when choosing a lens, is the maximum aperture. It's listed in the lens's name as the F number/fraction. For example, your current lens is 18-55mm F3.5 (to) 5.6 (depending on the zoom). The two lenses in question are very similar.
Another thing to consider is the lens's ability to give you great image quality. Not all lenses are created equally...some are just designed to be better. To find out the quality of a lens, you have to do some research, but in general...the price is a good indicator. The better quality lenses just cost more.
So when you are looking to upgrade from the lens that you have...you can consider upgrading the zoom range, or you could consider upgrading to a lens with a larger maximum aperture (lower F number) (this would allow for faster shutter speeds, which would likely mean sharper photos). You could consider upgrading to a lens that can give you better image quality.
You will usually have to choose some, but not all, of these options.
For example. As nice as it may be, to have a lens that can give you wide views for landscape, as well as being able to zoom in close for wildlife....a lens that can do both those things...will likely have lower image quality. On the opposite end of that scale, you will find 'prime' lenses (non-zoom). So a lens that is fixed at 50mm won't zoom, but the image quality will likely be much higher than a regular zoom lens. It would likely have a larger maximum aperture, which can give you faster shutter speeds and a shallower Depth of Field.
A common choice is the Canon EF 50mm F1.8. It's a bit of a cheaply made lens, but it's inexpensive and the image quality is great for the price.
Also, you might consider adding a lens, rather than replacing your 18-55mm. For example, a common choice is the 55-250mm. Then, with both lenses, you have the option of anything between 18mm and 250mm.