Blogger (www.blogger.com) is a free publishing platform owned by the giant company Google. A publishing platform means a comprehensive tool to publish articles and web-pages in a domain / website. Therefore, users don’t have to use the old school file transfer protocol (FTP) to run their websites, the platform takes care of everything.
This platform does not have to be used with Blogspot, it can also be used with any other custom domain (such as http://www.yourname.com). The system is similar to Worpress.ORG: free publishing platform.
Blogspot (www.blogspot.com) is a free domain service provider owned by the same giant: Google. The free domain provided is actually a sub domain (like example.blogspot.com). This company is to support Blogger in delivering free blogging service.
In summary, Blogger is a free publishing platform, while Blogspot is a free domain service provider. Blogspot have to be used with Blogger, but Blogger doesn’t have to be used with Blogspot. However, both are designed to work together in providing free blogging experience for their users.