Modulating an Osc. with itself

[Moolla]

Osc 1 and 2 are both sine waves with exact same parameters.

Case 1: I modulate Osc 1 using Osc 2
Case 2: I modulate Osc 1 using itself (Osc 1)

They sound different, Case 2 sounds 'brighter'.
Is it because in Case 2, Osc 1 recursively modulated itself?
If it does, is there a limit to the recursions?
Or why is there a difference in the sounds?

[nucleon]

Indeed in Case 2 it is effectively modulating i...