In both cases, the actual movement of data is done from the Vita, in its own "Content Manager Assistant" app. The PS3 displays only the above screen. I plugged the handheld into the PS3, moved some photos around (the Shadows of the Damned and ... Hot Pockets promotional backgrounds, and 3D Dot Game Heroes screens being all I had), and otherwise looked around the menu, capturing screens of the process in the gallery below. Enjoy looking at pictures of menus!
You'll notice that the "music" and "photos" pages look slightly different. When you open up those areas to browse, it actually opens up the Vita's separate "Photo" and "Music" apps, leaving the Content Manager running in the background.