Your question could be interpreted in several different ways. I’ll try to address each of them here.
Moving and deleting
By “moving” a file to an external disk, I’ll assume that you mean that you copied the file to that external disk and then deleted that file from your original machine. In a situation like that, the original file may still be undeleted. For example, in could be in the Recycle Bin. However, even if you empty the Recycle Bin, there’s a slim chance that your file is still on the computer.
A quick solution to that piece of the puzzle would be to use a secure delete program to delete it for real, or use a free space wiper after you’ve deleted the file.
Formatting versus formatting
You asked about formatting; there are actually two different types of formatting.
A quick format makes very minimal changes to the disk; it only erases the root directory. A quick format basically marks the entire disk as empty, but it doesn’t actually overwrite anything else that’s on the drive. As a result, your file could still possibly be recovered.
A full format will overwrite everything on the hard drive. (You can tell the difference because a full format is going to take a long time). While there are techniques that can sometimes recover files from a fully formatted drive, they typically require special equipment and money.
Now, when you say, “formatted that drive” I’m not sure whether you mean your computer hard drive or the external drive. In either case, I don’t recommend using a quick format for what you want to get done. Use a full format, or a free space wiper, which can usually be configured to even be more thorough then a full format. Why more thorough? Free space wipers can usually be configured to overwrite the data multiple times, while a full format will only overwrite the data once.
Regardless of which drive it is you’re formatting, just remember that the file or the remnants thereof could still be on the other one.