No. You have a regular Shield that plugs into the MEGA2560 as Nature intended.
"Arduino Nano" has no headers. Just manually connect signals like a Uno.
It is pretty straightforward. This Shield will plug into any Uno, Leo, Mega2560, Due, .... These are known as "Arduino Shields" or "Uno Shields". Each male pin has a corresponding female socket.
The "other" kind of Shield has a set of 2x18 pins. It only fits in MEGA2560 or a Due. These are called "Mega2560 Shields"
If you had bought a non-Shield display, you would have to wire each signal to the Arduino by hand. (Probably with a level shifter in each line)