A standard CW filter operates on the IF (RF after at least one stage of downmixing, but before demodulation). Elecraft's APF operates on the demodulated audio.
The reason most filtering is done at IF is because making a nice sharp filter becomes easier the higher the filter's center frequency (within reason). In Elecraft's opinion, a filter with the more gradual roll-off implied by a center frequency of only ~1kHz is beneficial to CW copying, when used in addition to the ordinary IF filter.
Since this is a bandpass filter, it's the exact opposite of a notch filter, but other than that, it's the same :)