An arranger keyboard is a portable-style keyboard designed to provide auto-accompaniment that can produce a backing track matching the rhythm, tempo and style of music being played. You can play a solo composition but have the feel of playing with other musicians.
A synthesizer, on the other hand, is an electric keyboard that can generate a wide range of sounds. Synthesizers are also smaller and portable.
The main difference between an arranger keyboard and a synthesizer is that an arranger is designed for solo performances while a synth is designed to be played with other musicians.