...go into a bar and order a drink. Which one's the odd one out?
The answer is the guaranteed maximum price contract because at least there's some evidence (however dodgy) that the other two might actually exist.
Because whatever your views on humanoid creatures living wild in the Himalayas or the traditions that have sprung up around a beatified fourth-century Greek bishop called Nicholas, I hope you agree with me that a GMP contract really is an urban myth. The reason for this is pretty simple and goes to the core of how construction contracts work. Most (all?) contain clauses acknowledging that things can happen - let's use NEC-speak and call them all compensation events - that might entitle the contractor to more time, more money or both. And, although different projects might allocate risks differently, there will always be some events that allow the contractor to claim. That's because, at the very least, the law doesn't allow the client to prohibit (either deliberately or inadvertently) the contractor's work (by the late delivery of information, say) and then require the contractor to stick to its original bargain.
Which raises the question of why industry still uses the term. Ask a non-construction expert - a lay client for example - what they think the phrase 'guaranteed maximum price' actually means and most will say something along the lines that it does exactly what it says on the tin. And yet it doesn't. And it can't. So why use the term?