Paul,
I suggest you use Google to educate yourself
properly, but here is my quick and dirty
summary:
An audio recorder will record audio(usually in
wav format). Think of it as a digital tape
recorder. You connect the audio outputs of
your keyboard into it and record away.
A sequencer uses MIDI and usually uses MIDI cables,(although USB is also becoming more common). Think of it as a digital player
piano roll. It actually plays the notes
of the synth it is connected to.
If you think you want both audio and MIDI, the best way to go is software, and I would
highly recommend Cakewalk Home Studio.