What's the difference between an MRI, Pet and Cat scans?

what's the differences aside from their names?

I have had a MRI and a CAT scan.

The CAT scan involved them injection me with radioactive material which later made me sick as a dog. The machine was a thin round whole, in which the scan moves around. Your not imprisoned and the machine was less then a metre long, they focus it directly on the target area.

The MRI scan once involved a die and the other time did not. It was like a big coffin, very claustrophobic, I hated it, it was noisy unlike the CAT scan and took over 1/2 an hour. It sounded much like a construction site and made me quite anxious.

I have also had an Angiogram, which was sort of like laying on a big photocopier, then the top part spun around you, it was quite time consuming too and made me feel a bit dizzy.

That might not be what they actually are used for or what they do, but its the personal experience if that's what your after.
My tests were used to find out why I was paralysed, I had in fact torn my right carotid artery which had left the left side of my body paralysed. The CAT scan, was no use in finding this, the MRI was of most use.

EDIT~ The most detailed would be the MRI, it gave a more accurate picture of my injury to allow diagnosis.

MRI = magnetic resonance imaging - uses magnetic field and radio waves
PET = positron emission tomography - like an x-ray but you have radio-isotope in your body
CAT = computed axial tomography - computers generate 3D image
The most detailed is none of the above - the answer would be fMRI - or functional MRI when it shows moving processes in your body instead of still pictures....