What is an arpeggio? A broken soul
A strumming patter
A broken chord
All notes played at the same time

Well every arpeggio is a broken chord, but not every broken chord is an arpeggio.

A broken chord is just as it sounds: a chord that is broken up in some way, shape, or form where you are not playing the the full chord at once.

An arpeggio is a specific way of playing a broken chord that has a defined texture to it. While the definition is not a very strict, it is typically characterized by playing one note of a chord at a time that aren't sustained in a pattern. While you may see an arpeggio where two or more notes are played at once or some notes may overlap in a sustain like manner this is more an exception then the norm. An arpeggio is also typically rhythmically straight or if not repeated in a pattern. It's really the only way instruments that can only play one note at a time can play a broken chord.

Explanation: