In an attempt to determine the difference between the two, Wikipedia left me confused. Can you help?
A sequencer is a tool where you can record and edit the "definition" of music. Think of a sheet of music - It tells you what notes to play, how long each note is, and how loud or soft to play. Now imagine that you can specify each of these parameters very precisely for each note. That is what a sequencer does.
A synthesizer generates audio (sound). You tell it what note to play, how loud and how long to play it, and what sound to use, and it generates the waveform of the specified sound at the specified pitch and volume for the specified duration.
There are several ways to tell a synthesizer what to play. Some synths have a keyboard that allows you to pass this information to the synth by what keys you press, how hard you press them, and how long you hold them.
This article also has a good comparison.