What's the difference between Holding Point and Hold Short?
The U.S. and holding point
It depends on the locale and context. For taxiing in the US holding point is not used as the FAA ATC manual refers to it as an ICAO term for a visual (or otherwise) holding point in the sky.

HOLDING POINT [ICAO]− A specified location,
identified by visual or other means, in the vicinity of
which the position of an aircraft in flight is
maintained in accordance with air traffic control
clearances.


Elsewhere and hold short
Elsewhere for taxiing, holding point is where the intended departure will take place from a runway. Check eurocontrol.int for examples (direct linking not available), but here's an example they give:

TAXI TO HOLDING POINT [number] [RUNWAY (number)] VIA (specific route to be followed), [HOLD SHORT OF RUNWAY (number)] or [CROSS RUNWAY (number)]. [REPORT VACATED]


Taxi to holding point A, runway 36, via A.

That means take A all the way to the end where it meets runway 36 and stop at the hold short line or behind whoever is ahead.

Taxi to holding point C, runway 36, via A and C.

Here the runway was shortened (an intersection departure) and the pilot will hold at C and then line up from C when cleared.
Report holding point means report when you get there.

Tower, Stack 1 is at holding point A, fully ready.

Hold short is the same everywhere and applies to any intersection or runway on the way to the runway/gate.

Taxi to holding point A, runway 36, via A, hold short C.

Here the pilot will hold where C meets A and awaits clearance to continue.

Hold your position is an instruction to stop right now.
Some airports employ LAHSO (Land and Hold Short Operations), where a hold short line exists on the runway you are landing on.

Example: Cleared to land runway 27, hold short runway 22L.

Example in Boston Logan (blue circle):