This page describes the differences in detail:
https://support.google.com/accounts/answer/72709?hl=en
In a nutshell, when using Google Apps you own the domain and sign up for Google Apps (email, docs, calendar, etc) for your business. Your email service is hosted on Google's gmail infrastructure.
With a simple Google Account you can sign up using any old email address hosted anywhere and Google send a confirmation email to the address that you specify. Once you click a link in the confirmation email your Google Account is activated and you can then use the GAE dashboard to invite the account to be a developer on your app.