What is the difference between DVD r 16x recording speed and 48x?

The x48 speed you are referring to is CD speed. DVD x1 is 1350 KB/s, while a CD x1 is 150 KB/s.

DVD x16 is 21.6 MB/s (21.094 MiB/s)

CD x48 is 7.2 MB/s (7031.25 KiB/s)

Do keep in mind that these are SI units, and 1KB = 1000 bytes. In computer units, 1 KiB = 1024 bytes.