Do Canon lenses have different sized attachment ends?

Are there different openings on dSLR-class cameras?(Canon and Nikon?)
I heard something about all Nikon lenses having the same attaching end(sorry if I'm using the wrong terminology) opposed to Canon lenses not? So Canon lenses differ in attaching end sizes?
Also, which do you suggest: Canon, Nikon, Sony, Fuji-Film?

In general, most manufacturers lenses work on most of their cameras but you can't just assume they do. Canon does not work on Nikon and vice versa. Other brands make lenses for Canon and nikon. Tamron and Sigma are big in that area.

It's called a mount, and you have to get lenses that have the appropriate mount for you camera. So if you have a Canon camera you have to get a Canon mount lens, Nikon to Nikon, Sony/Minolta to Sony/Minolta etc.

It's just a little more complex than this as we're in a transition era where auto focus motors are moving from the camera body to the lens. Top end cameras will tend to support both mechanical couplings and electronic, while some at the bottom of the market will only support one or the other. The manual that comes with your camera would tell you what type of lenses will fit. If you buy you lenses from a bricks and mortar shop you can usually mount them first to make sure they fit and are fully compatible.

The above is more-or-less right, but there are a couple of exceptions;

Canon and Minolta (now Sony) Changed their lens mount when autofocus came in. The old Canon FD mount and Minolta MD do not fit their autofocus cameras.

Pentax and Nikon merely added extra connections to their existing lens mounts so, in general, Pentax lenses from 1975 on and Nikon lenses from 1959 on fit their cameras with a few exceptions and loss of functions.

Olympus kept their lens mount the same until the advent of digital when they went to the four-thirds sensor. All 35mm cameras use the OM mount but are incompatible with their digital models.

Fujufilm stopped making interchangeable lens cameras a long time ago.

Lenses are not interchangeable between manufacturers.

The only way to choose a camera is to work out how much you want to pay, find a couple of likely candidates and visit a dealer who'll let you handle them, picking the one you like best.