We may be using different definitions but the same word - which causes confusion. I'm reading V.S. Littauer's "Common Sense Horsemanship". In one spot, he argues - correctly I think - that many of us who use the word 'collection' put an improper meaning to it.
"...you hear people say that they collect their horses before the jump or in a trappy situation in the hunting field...One in a thousand of those who use this word so easily, really collects his horse. The best of the rest merely refer to the ability of their horses to change their balance by gathering themselves, which is known as 'coming back' and which requires only a simple technique on the part of the rider....and you will have to argue hard to prove that it [collection] is necessary for cross-country riding and jumping." - page 203
Now arguably, if 999 out of 1000 use a word for one meaning, and only 1 in 1000 uses it correctly, then maybe the definition of the 1 is wrong.
However that may be, the OP was referring to jumping. And with my very limited horses and limited riding skill, it is a safe bet that I NEVER 'collect' my horse in the sense a good dressage rider would. That is why I used the term 'gather' earlier - that change of balance where the horse coils up, and gets ready to use his hind legs to power the anticipated change - acceleration, jump, sharp turn, etc.
I think it would take a very special person to collect a horse in the Olympic sense using a curb or training it without a bit - although a well trained horse could then PERFORM it without a bit.
Since the OP referred to jumping, and since I freely admit my limitations, I just wanted to clarify what I meant. I have never ridden a collected horse in the dressage sense of the word. I have ridden my horse where they gather themselves and get ready to use their hind end. That is the momentary 'collection' that I meant.
BTW - I may try to train myself to use the word 'gather' instead of 'collect'. One of my pet peeves is someone applying two different definitions to one word, and it makes sense to me to save 'collect' for the more Olympic-style, dressage collection.