I've noticed for 2 moves, that they change from physical to special moves, gen 2-3 Physical to gen 4+ special according to the site.
- Sludge Bomb
I thought both were special, but the sites show as physical moves for gen 2-3. Is this Correct?
See TM move sets for Venomoth and Tauros Gen 3;
Prior to Generation 4, a move's category was determined from its type. For instance, all Normal and Poison moves were physical if they weren't status moves, and all Dark and Water moves were special if they were not status moves. The full list of which types were physical and which were special can be found here. In Generation 4, the "physical-special split" happened, and a move's category was determined individually, rather than being based on its type. This was beneficial to Pokemon like Sharpedo, who prior to Generation 4 had no way to effectively use their better attacking stat.
So in short, yes, this is correct. There is no error.
Hope I helped!