The purpose of right hand rule was to have a idea about the magnetic field around the current-carrying wire
Used for finding the direction of the magnetic field around a straight current-carrying wire.
Right Hand Palm Rule - Visual Representation

The Thumb represents the current
The index finger represents the magnetic field
The underneath the palm represents the force of magnetic field on the conductor
Unlike left hand rule that talks about force of magnetic field the right hand rule is mostly about the force on moving charge / current
Right Hand Thumb Rules
The right hand thumb rules is different than the normal right hand rule

Both right hand palm rule and right hand thumb rule is different
The thumb represents the direction of current
The underneath of palm represents the direction of magnetic field
Difference between right hand palm rule and right hand thumb rule is that the thumb rule focuses more on direction while on the palm rule it includes force






