Most, but not all, of OSX is not case-sensitive. When you format a disk you can choose a case-sensitive file system, but it is not recommended for the main OSX partition because some applications will fail (different parts of the application mistakenly use different case when referring to the same file).
If you need a case-sensitive file system for some special purpose, you can use another partition, or create a disk image file, with a case-sensitive format.
You can use upper and lower case in the short name when you create the account, and it will give your home folder a name with the matching upper and lower case. Changing the short name or home folder name can create problems. Often it is easier to just create a new account and copy files over.
Some parts of OSX (e.g. passwords) are purposely case-sensitive, some accidentally (some applications treat files differently if the extension is upper-case). Terminal commands are Unix, which is case-sensitive.
