»I noticed that I can see a picture I've deleted from my computer. «
Please elaborate. As we cannot see what’s going on on your computer that »description« does not seem useful …
»When you pull a picture into photoshop does it save a duplicate image of your photo?«
While an image is open in Photoshop Photoshop stores it in RAM and (if RAM is insufficient) on the Scratch Disk/s, so one could say it exists a second time, and depending on the »Automatically Save Recovery Information …«-Preferences-setting there may even be an additional back-up-file, but I am not sure what you actually mean.
Say you have a JPEG that's called, "image.jpg." You open it in Photoshop and go to save (using Ctrl/Cmd + S). Photoshop will default to its own format (which is PSD) instead of the document's original file type when saving this document, therefore leaving the original document untouched. If you don't intend to keep the original, you'll have to delete it yourself *unless* you save with the same file name and file type in the same location. (Photoshop will always ask if you want to replace.)
You can also use Image > Duplicate on the menu bar if you're feeling paranoid. 🙂