From Wikipedia:
Vibrato (Italian, from past participle of "vibrare", to vibrate) is a musical effect consisting of a regular, pulsating change of pitch. It is used to add expression to vocal and instrumental music. Vibrato is typically characterised in terms of two factors: the amount of pitch variation ("extent of vibrato") and the speed with which the pitch is varied ("rate of vibrato").
TREMOLO alters the volume of the note (not it's pitch). This was originally achieved by a Leslie Speaker:
From Wikipedia:
The Leslie speaker is a combined amplifier and loudspeaker that projects the signal from an electric or electronic instrument and modifies the sound by rotating a baffle chamber ("drum") in front of the loudspeakers. A similar effect is provided by a rotating system of horns in front of the treble driver. It is most commonly associated with the Hammond organ.
In short: Vibrato deals with change in pitch. Tremolo deals with change in volume.
With the Farfisa organ I had years ago I had a Leslie Speaker Cabinet, which as I have described above created the Tremolo mechanically. This takes some time as motors have to speed up and slow down. I used to love to hear this effect done in this way. The trouble with 'electronic' Tremolo is that the change happens 'in an instant' .. and this does not sound the same!
If you like organ sounds then listen to what the Leslie does to the sound when switching between fast and slow Tremolo.