OK, a little more time now.
An analogue servo reads in a position demand (pulse width) every 20mS (50Hz) and uses that to determine where the servo should be. The "error" (actual position vs current position) is calculated (using an analogue method) by a pulse amplifier to derive a motor drive.
Hence, drive is only available when there are pulses present and updates to motor torgue can only be made every 20mS.
In a digital servo, there is "intelligence" within the servo.
How much, depends on the exact model of servo chosen.
Typical benefits include:-
The ability to hold postion even when no pulses present.
(this can either be last good position or some predefined 'safe' position.)
Many digital servo offer the ability to 'program' parameters such as maximum speed. (you don't always want a servo to move very fast).
The existing servo signal standard (1mS to 2mS every 20mS) has been around longer than I have. Models have come a long way since then and trying to fly a helicopter at 150MPH upside down 2" from the ground requires a fast response to avoid tears. An update every 20mS is no longer fast enough. SOME digital servos will accept an update rate of several 100 kHz which gives a much faster response to position demand changes.
A word of caution:
Some servos are advertised as digital but offer ZERO advantages over analogue. Whenever buying a servo, read the spec.
As with HiFi, would you prefer a cheap digital CD player over a quality analogue vinyl record deck?