Wow: The whole process of getting iOS apps up and running is making my head spin.
I have an app that works well in simulator.
I have signed up to AppleDev, and I have created certificates.
I built a universal app, and it synched to my iPhone and works.
I plugged in my new iPad and although it tries to install, it always says that it failed.
Both are listed on the apple dev site as devices I want to use for testing.

Possible issues:
I used iTunes account A on my iPhone, and created a new one for developing.
Sometimes my old account shows up on the iPad, even though as far as I know, I wasn't logged into it when I hooked up the iPad.

Anyone have any ideas why it would work on one but not the other?

The provisioning profile you are using may not include your iPad as one of the listed devices. Double check that it is indeed registered and checked enabled as one of your allowed devices for your particular development profile.

You may also want to delete and re-download/install your provisioning profile in case you added the iPad after you already installed your original profile (which only had your iPhone).

Marvellous!
Thank you very much, that was the hint I needed.
I did add the iPad after creating the provision.
I went back and downloaded a new one, but it still didn't work.
After a fair amount of cold sweats and swearing, I went back and found an 'Edit' button.
In there, I found that although the iPad was listed, it was unticked.
So one tick, a save, and a download later, and I can run the test app on the iPad.

(I see that there are some differences between the simulator and the iPad: for instance the splash screen doesn't fit, and it's rotated by 90 degrees on the iPhone, but those should be small potatoes, and for another post if I struggle)

Thanks!