Hi, don't know if it differs on the new model, but if you select S it allows you to select gears manually, also with Dynamic selected car will hold lower gears for longer, allowing more spirited progress, I usually use mine in Sport and Dynamic all the time, being able to select gears is also useful to allow engine braking to assist long hill descents, Tony.
Putting the gearbox into sport mode makes a great deal more difference to the driving experience than Dynamic mode. Once you start driving in Sport it runs in much lower gears so performance is rather more twitchy, and you always have masses of power instantly available as you are running around at 3-4000 rpm and its even more prone to just sitting at 6000rpm and screaming up through the gears when you accelerate than usual (I have a P250) . Its fun in short bursts, but the related fuel consumption is spectacular. I have mine set to allow manual gear selection only in S mode, I very occasionally use manual gears when going down a really steep long hill to get a bit of engine braking. Otherwise manual gear shifting isn't a great experience with a 9 speed box and I can't really see the point in any other sort of normal driving.
Its really difficult to know exactly what Dynamic mode does, but I'm not at all convinced it makes any practical difference to how the gearbox works - I think thats all down to selecting Sports mode. I found this marketing spiel from jaguar, which predates the e-pace: https://www.jaguar.co.uk/about-jaguar/jaguar-stories/adaptive-dynamics-and-configurable-dynamics.html that suggests it does all sorts of clever things with adjustable dampers and steering. Certainly the car feels a bit more engaging in Dynamic, but that might just be because my dials go Red (digital dash).
I tend to find that there is less hesitation to change down the gears in Dynamic when pressing the accelerator.
So in Sport it holds the lower gears longer and in dynamic it selects them quicker when pressing the accelerator?
This also matches my experience with my XE 180D where I used Dynamic all of the time to overcome the hesitation issues.