The Finder is the file system on the computer. All the files, folders, pdfs and everything can be found using the Finder.
When you search with Spotlight and click on the one you are interested in the file's location will show at the bottom of the window. It will show all the folders so you can follow them like a map or path.
See this image to see what I'm talking about:
At the bottom yo can see that file I selected is in my home folder (sgand), then in TeachTech folder, then in Customer Stuff folder, then in Google folder. You can find any folder like that by starting with your home folder.
First, click on the blue face in your Macintosh Dock.
Go to the Go Menu > Home
A window will open showing all the folders in your home folder, then you can open the ones shown in your Spotlight window.
IN the Adobe programs the recent items list is just a list, not the real things. So, as you view other PDFs the older ones will disappear on their own. Open more PDFs and you will see the list change. Getting the real file to the trash as described above is the way to "banish" it forever.
Edited by Steve on 10/1/2010 at 5:34 PM EST