As for connections between the two words, it's possible that *balingag* (illogical thinking) could contribute to or trigger *balingaw* (venting frustration through destructive behavior). Someone experiencing frustration or anger due to their own irrational thoughts or actions might lash out at objects, leading to *balingaw*.
Conversely, *balingaw* could also be a manifestation of the emotional turmoil resulting from *balingag*. In this sense, the two words might be related in that they both describe aspects of emotional or cognitive dysregulation.