I think where you are getting confused is the fact that all the names have deeds in them. There are many ways of getting a deed to a property it all depends on who gives it to you and what the process involved was. Below is a quick description of the three different ones you asked about
A foreclosure deed is what you get at an auction to show you own the property
A grant deed is what you get after a lender or person has sold or given you a home. It has a lot of information and is a good way to prove you own the property.
A quick claim deed is what you get after you given/sold the home. It has the least amount of paperwork but at the same time offers the least amount of protection.
There is a good site called http://www.investopedia.com
which I used when trying to understand the different vocabulary for real estate.