The Arduino Mega 2560 is an older form of the Due. It is based on the ATmega2560 processor (hence the name).
Like the Due, the board supports a massive 54 digital I/O ports, of which 14 can be used as PWM output; 16 analog inputs; and 4 UARTs (hardware serial ports). It uses a 16MHz clock and has 256KB of flash memory
The Mega 2560 is essentially a larger form of the standard Arduino (Uno, Duemilanove, etc.) and supports the standard shields. The figure shows the Arduino Mega 2560, board.
Interestingly, the Arduino Mega 256 is the board of choice for Prusa Mendel.
The Arduino Mini is a small form-factor board designed for use with breadboards. Thus, it has all its pins arranged in male headers that plug directly into a standard breadboard.
It is based on the ATmega328 processor (older models use the ATmega168) and has 14 digital I/O pins, of which 6 can be used as PWM output, and 8 analog inputs. The Mini has 32KB of flash memory and uses a 16MHz clock.
Unlike other Arduino boards, the Mini does not have a USB connector.
To connect to and program the Mini, you must use a USB Serial adapter or RS232-to-TTL serial adapter. The figure shows the Arduino Mini.