The most correct term - according to IEEE and IEC - is ASD (Adjustable Speed Drive). This refers to the electronic equipment used to regulate the operating speed of the motor and driven equipment by controlling the frequency and voltage applied to the motor.
NOTE that other terms in common use include (but are not limited to): VSD (Variable Speed Drive), AFD (Adjustable Frequency Drive), and VFD (Variable Frequency Drive), they are referring to the same motor drives, just different names.
All refer to "generic" drive topographies (e.g. how they are used and how they work), rather than specific details (such as current-source or voltage-source, multi-level, etc.)
To answer the specific question posed: there is NO difference between a VSD and VFD in terms of what it is designed to do. There MAY be differences based on specific internal components/construction and how it achieves that goal.