I guess we could discuss the theories of this till the cows come home and maybe should start a new thread but I still say the are the same, well the basics anyway.
BUT, saying one is used to propel a car and the other pumps water isn't a fair comparison.
One pumps air, one pumps water is more like it and in that case i say 'the same'
I'm only thinking of one side of the 'car' turbo at a time mind you. Not as 1 powering the other.
...besides, if you had just the compressor side of the turbo removed and somehow powered up and water feed into it, i bet it would pump water for as long as it was powered. Maybe not very well but it would.
Get Sydney Kid to try it! HAHA !