Lost internal storage space on my Xperia Z1 Compact
Android's internal storage is made up of many symbolic links. They point towards different locations of your phone's storage.

/mnt/sdcard internally links to /data/media. This directory just contains your user data but no applications or application data.
/data/ contains multiple directories containing the apps (/data/app) or the app data (/data/data) that all contribute to the used storage.

What you see using df is the total storage statistics of the whole partition, even though you run it on /mnt/sdcard.
Citing the Linux manual: df - report file system disk space usage.
This means it takes into account all files and folders on that partition even though you are using a directory of the partition as the parameter.

Conclusion: df returns the statistics for the complete partition, but you are just looking at one directory inside of it.