Doug, it sounds like you just downloaded the software but possibly didn't install it after the download. That may be why Thunderbird doesn't show up in your Applications folder.
To find the software you downloaded, just look in your Downloads folder which is in your User folder (unless you downloaded to a different location). If you do want to install the software that was downloaded, then just move it into the Application folder in the main drive. Once in there you can doubleclick it to start the program or with some software it will continue with an install process.
Hope all goes well