Duffy, there is a slight difference. Carrot stick is basically a lot heavier than an ordinary whip, and the string lands softer on a horse than that of a whip for the same reason. Therefore, I find carrot sticks better for beginners, because they are too uncomfortable to be overused and to heavy to be moved fast (unless the user has strong hands), thus a horse isn't traumatised by unnecessary and heavy whip usage and it is quite good for young and easy to scare horses, too (in my experience).
For skilled people and experienced horses, however, I'd suggest a good whip or, as I prefer, a Honza stick (Honza Blaha, a chechz NH horseman) - a lighter and easier to use kind of "carrot stick". And in a better colour, too. :P
But like you said, it depends on the hands that use them... a lunge whip can be gentle, a carrot stick can be harsh, but they're both used for the ultimate end goal.. or so Savvy says, I didn't think PP 'hits' his horses.. I thought it was all about asking
Many ways to skin a goose, but in the end, a carrot stick and a whip are much of a muchness.. different colours, different weights, but they're still the same thing. I can use my whip as lightly, or as heavily as I like or need to... what I'm trying to say is Parelli isn't the be all and end all, and where I'm not an expert in the matter, I don't understand why people use the term 'carrot stick' to make it sound cute and cuddly when it principle its a whip.
Also ref the hitting, Savvy said the aim, I think in another thread or this one, is NOT to scare our horses.. the first time you whack with that whip, carrot stick etc when you have asked, told, DEMAND of course the horse is going to have a moment to itself, and hopefully not do it again.