Do Streaming Files Actually Exist?

Everyone speaks about video and music streaming, however I am under the understanding that there isint actually any such thing as legitimate real time streaming, ALL files are saved to the disk or the RAM. If this was not the case, disrupting your Internet connection would cause an instantaneous crash of the streaming media, and well, I have had my Internet crash a lot of times while viewing streaming median and in every case it continued to play for some time.