Why are extended ASCII values on my computer accurate until 188?

I want to be able to type special characters, and judging from this list, only from 0 to 188 (inclusive) do the characters I get out match whats on that site.

Depending on your computer you might be using a different ASCII code page.

ASCII had (rudimentary) support for languages other than English in the form of code pages which can allow characters beyond the standard set. Windows can be switched to different languages which will change the ASCII set used. For a list of common Windows code pages see this section in Wikipedia: Microsoft Code Pages

Unicode goes beyond the need for code pages by enlarging the character set to allow most characters in every language to be used in one single character set, but support for code pages at the lower end could be achieved by mapping the standard ASCII set (below 255) to their counterparts depending on the code page or language selected in your operating system.