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There are two special sidebars, designated only by name. Avoid renaming these unless you know what you're doing. There should by one of each.
One is the Blog Sidebar, which appears on all the blog pages. It has two new sidebar item types in addition to the normal three: Blog Archives and Blog Categories.
The only special thing about the Default Sidebar is that it's selected by default when creating a new Content, Area, or Home page.
There are three item types for all sidebars, plus two more for the Blog Sidebar.
The link lists work exactly the same, except the resulting sidebar item may have its links laid out as one or two column list.