Windows 7 - Effect of storage serive on mobile devices

Many companies offer remote storage services (e.g., SkyDrive, Box, etc) in their server. So we are able to upload tons of pictures, videos, music and documents to there. Those files are also accessible by iPAD, iPhone, and other mobile devices. In another words, we could play uploaded videos on iPhone and iPAD. My question is whether the uploaded files also use up memory space in mobile devices (e.g., iPhone and iPAD). I thought that in order to play music or videos on iPhone, these files also must reside in mobile devices. Since mobile devices have a limited space (e.g., 16GB for my iPhone), some problems could occur in my iPhone if files more than 16GB are uploaded to server of SkyDrive or Box. Am I wrong?

I don't really use those services, but I would assume that the are streamed to your device, similar to when you watch videos via youtube.