Everytime I go and download something from the net, the 'do you want to run or save this file' window pops up. Unless I know for sure I want the file on my hard drive, I click run, download it to my deskop and delete it after I install or save it to a folder. Both save and run will lead you to the setup for the program and install it on your computer, but the difference is where the setup file opens from.
To learn exactly what run and save are, just
If you click "Save" you can specify where the setup file goes (My Downloads or the desktop). From there you could put it on a disk just in case you need to reinstall it or want to put it on another computer.
By choosing "Run" the setup process starts once the setup file is downloaded to your temporary internet file. When you empty your temp file the setup download goes away. This is great if you aren't a download nut job, but you should be cleaning out your temporary files regularly anyways so that your temp folder isn't filled with downloads.