I apologize, in advance, for creating a zombie.

They must have all different blocks, crankshafts, pistons, etc. All of the lower parts would have to be different because the 1.6 cannot be bored or stroked to those dimensions safely.
If you look at the engine of the Chevy Cruze 1.6, it is the exact same engine as in the Aveo, but has nearly 10 HP more output. The only difference that is visually noticeable is the airbox assembly.

It has to be the tuning, in combination with less restriction in the intake system. Most likely for emissions reduction for the American market. The 1.8 is producing more power per liter of displacement than the 1.6 , it would have to come from that.