You seem to be confusing downloading and running.
I seem to remember that you're using Firefox. When Firefox downloads a file it shows a progress box. While the download is taking place you can right-click it to locate the file. Unfortunately, if it's a small download, the progress box is emptied before you have chance. There have been many complaints about this.
When you click 'run' you are not starting the download, you are installing the downloaded file.
Downloading in both Chrome and IE is superior, in that both offer you a list of all downloads along with options to locate and/or run/open the files even after the download is completed.