Categories are dealt with via “Category Groups”.  You create a Category Group and then create individual categories within it.  You can create as many Category Groups as you want and you can have as many individual categories within each Group as you want.

Categories in two different groups can have the same name (say, a “news” category in two different groups) but the content inside the category will not be the same.  They are separate categories and only happen to have the same name.

When you create a weblog you can assign a category group to it.  Weblogs may have more than one category group assigned to them.  Further, the same group can be used with more than one weblog or you can create a separate group(s) for each weblog.

See Category Management in the documentation.