Simply put, the ideal polarizable electrode is characterized by charge separation at the electrode-electrolyte boundary and is electrically equivalent to a capacitor, while the ideal non-polarizable electrode is characterized by no charge separation and is electrically equivalent to a short.
Any transient current that may be flowing is considered non-faradaic.
[1] The reason for this behavior is that the electrode reaction is infinitely slow, with zero exchange current density, and behaves electrically as a capacitor.
[1] An ideal non-polarizable electrode, is a hypothetical electrode in which a faradic current can freely pass (without polarization).
The reason for this behavior is that the electrode reaction is infinitely fast, having an infinite exchange current density, and behaves as an electrical short.