I've always heard it as:
Billy was a chemist's son
But Billy is no more
For what he thought was H2O
Was H2SO4. Billy was a chemist's son
But Billy is no more
For what he thought was H2O
Was H2SO4. Little Timmy took a drink
But he will drink no more
For what he thought was H2O
Was H2SO4"thought was H20 was H2SO4" is identical in all the variants I found after the mid-20th-century. Most, but not all, have "What he thought was H20 was H2SO4". It seems like they "perfected" that part and it hasn't really changed since.
But the rest is very changeable--a few variants mention chemists and most mention a male name of some sort, but most have nothing else in common.