In this case the change is significant. If you just cut squares you can do quite a bit and it leads to significant ideas related to continued fractions, but you will only get finite continued fractions (rational numbers) and periodic ones (quadratic numbers). Cutting rectangles and squares can give higher degree algebraic numbers, like the cubic number for the main spiral. I am working on a porrf that you can get all algebraic numbers.
The benefit of language experts and pedants has been to slow the rate of change in language. As a result we can read Shakespeare and other historical work in the original. It could be argued that this is itself an elitest point, especially about Shakespeare; however the ability to access the past without special training means that historical knowledge is not restricted to the elite.
As a BrE speaker, I do use "ise", but "ize" is not unknown, especially in science (I believe that the British published journal Nature has it as their house style). Recently I think it has been declining as it has been identified as "the american version".
The central difference is whether the process is by addition or subtraction. 3d printers, like the reprap, add material (for example melted plastic) to make an object. A router on the other hand removes material from an object until it is the required shape. As a result you can use many materials (like wood) that cannot be easily broken up into smaller parts and reassembled.
Although its true that a 3-Axis can do a lot more than people expect with some creative thought, there is a reason 5 (and higher) axis machines exist. For some tasks they can be essential.
For more formal programming Processing is a great learning enviroment: http://processing.org/
In both I would say the best method is to find challenges your son wants to undertake for himself. Learning to explore, play and fail is the way forward.