Is the 404 page the same as “well this is embarrasing” page?

This all depends on your theme. Most themes includes a 404.php template to display a “well this is embarrassing” page or an index of previous posts.

For example:

• My consulting site shows an index: http://jumping-duck.com/does-not-exist
• One of my client sites shows a basic “404 not found” error: http://votebode.com/does-not-exist

They’re both running the latest version of WordPress (3.3.2 as of this answer). Both sites define their own 404 behavior through a themed 404.php template.