can of worms truly opened ...
anglers and manufacturers use the terms with a bit of abandon, and there is some cross-over.
Historically a whip is a simple pole with a flexible solid top (flick tip). The line is attached directly to that tip and the rig is just shorter than the length of the whip. The whip is quite flexible to absorb lunges of bigger fish, but is mostly used for catching small fish fast.
A pole, on the other hand, is typically used with a rig much shorter than the length one is fishing - and sections are added and removed to put the rig out to the fishing position and bring the fish in when hooked. In ye olden days the line would be attached direct to a flexible top section - in the modern days a section of elastic is used as a shock absorber. Thus the pole can be used to reach great lengths (eg. 16m) even when sitting under overhanging trees. It is also more suitable for large fish - match anglers often land carp upwards of 15 pounds on poles.
so far so simple .... now the complications.
1. modern poles are very thin walled and would not cope with the rigours of casting in the style of a whip
2. generally modern poles are too stiff to use with a flick tip style
3. some anglers now use heavy gauge elastic within a specialist whip as insurance for bigger fish hooked and also where the average size is quite large (eg. 6oz upwards)
4. "system" whips have been around since the 80s - they are part telescopic and part take apart - allowing anglers to follow a shoal out whilst still using a flick tip setup.
5. having said that - on commercial fisheries some big weights have been taken by using just the end couple of sections of a pole with elastic and equal amount of line. This is generally referred to as "top 2" rather than a whip approach.
I guess that is now as clear as mud
Generally a pole is more adaptable to a range of circumstances, whereas a whip is a more specialist tool for catching small fish fast . The whip is simpler and more back to our roots as kids with a piece of cane and string.