Download with PDF and Adobe

When you download something that is in .pdf and using Adobe Reader...It "downloads" then shows it on the screen. I know that if I want to save it, I click to save and when on hard drive I want to save it, but..if I don't want to save it...where is that .pdf file now? It says it downloaded, but doesn't say where. Is it downloaded on my hard drive or is that just how they say "the file is open and you can look at it, but if you want to keep it you have to save it yourself" kind of thing? But where is that file been downloaded? On my harddrive? And if it is downloaded onto my hard drive some place, how do I find out where? And does it take up space? I have done many "downloads" to look at quilting patterns and some I have saved, but most I don't. Are those I didn't save on my pc anywhere?