Kinda funny watching people OOoh and Aaaah over something that Windows had launched 5 years earlier with Win95. The Mac/Windows flamewars back then were still as vivid as they are today.
It moved the whole window, but you could enable the effect you mention to save on system resources. (If memory serves right.)
I remember seeing the Betas in 1999-2000 or so and they were on an iMac and the whole UI barely worked.
And I think in 2004-2006 I was still turning the animations down or selecting the simpler ones. I maybe started leaving them on when I got a monster Mac Pro in 2006.