The glue I’m using says it dries in an hour but cures in 24 hours. What is the difference and is there benefit in leaving clamps on for the full 24 hours? Assume strength is important.
What is the difference [between glue drying and curing time]
As covered somewhat in this previous Q&A, How long does glue take to dry? all PVA wood glues 'dry' by literally drying initially and then there's a curing phase, where they undergo a chemical/structural change and harden more completely and get closer to their full strength.
So your glue says it dries in an hour and takes 24 hours to cure, so it's just holding the wood together at hour one and closer to being at full strength after 12, and has nominally achieved max strength after a day. But remember those times are averages, based on assumptions of temperature and humidity and wood moisture content. If any or all of those are different where you are your glue dry times will be different. Even using air-dried wood rather than kiln-dried wood your drying times will differ slightly, in the same workshop on the same day.
It's because you can't always know for sure what you're dealing with that you err on the side of caution, unless you have no choice. So it is good general practice to leave clamps on longer than you think is strictly necessary if you can. If there's nothing other than your impatience urging you to remove your clamps and go on to the next step resist the urge!
is there benefit in leaving clamps on for the full 24 hours?
Rarely. However, there's no downside to it either (other than the clamps being tied up and not available for other uses).
To put this more generally: it doesn't hurt to leave clamps on too long, but can if you take them off too soon.
As I cover in my previous Answer, if you take clamps off too early the glue joints can open up very slightly and result in greatly reduced joint strength. But one detail I wanted to add is that even an invisibly small shift in position or opening between boards can have a profound impact. So your joints don't have to be noticeable open or out of alignment for them to be weaker than they could be — which is literally stronger than the wood around them. This is the goal to aim for, whether the workpiece in question needs it or not. Because, why not?
From the Titebond website:
What is the clamping and drying time of Titebond Wood Glues?
For most of our wood glues, we recommend clamping an unstressed joint for thirty minutes to an hour. Stressed joints need to be clamped for 24 hours. We recommend not stressing the new joint for at least 24 hours. For Titebond Polyurethane Glue, we recommend clamping for at least forty-five minutes. The glue is completely cured within 6 hours.
Keep in mind that higher temperature, drier wood, and lower humidity speed drying time; while lower temperature, wetter wood, and higher humidity slow it. Stressed joints would be things like a bent lamination.