Your Google Account is used to log in to Google services. It is an email address and password combination, and it's generally what you'd type in any time Google asks you to log in. It can be a Gmail address, although it doesn't have to be. You can associate a new Gmail address with an existing Google Account, but you can't merge two existing Google Accounts together.
It is generally wise to go ahead and associate a Gmail account with your Google Account. Add any other email accounts you use (that haven't been associated with another Google Account), so that anyone sending you an email invitation to share a document will send the invite to the same Google Account. Make sure you are logged in to your existing Google Account before you create a Gmail account, or you'll accidentally make another Google Account!
As of this writing, you're out of luck if you've already accidentally made several Google Accounts. Perhaps Google will come up with some sort of merging tool in the future.
Google refers to their Web applications as "apps," so part of the confusion here is Google's fault. However, Google Apps ("Apps" with a capital "a") is a specific suite of hosted services that businesses, schools, and other organizations can administer using Google's servers and their own domain. Google Apps comes in several free varieties and a fee-based Premier Edition.
You log in to Google Apps using your work or organization email address. This account is not associated with your regular Google Account. You could use the same email address for both Google Apps and a Google Account, but it's unwise. You still have to log into your Google Apps account separately, but it can be extremely confusing to figure out if your shared services are going through Google Apps or your regular Google Account.
Your best option if this happens is to add a Gmail address to your Google Account and use the Gmail address to log in.
It is possible to be simultaneously logged in (using separate emails) to both a Google Account and a Google Apps account. Look on the upper right hand corner of your Google service to see which email address is associated with the service you are using.