"Response" can mean different things in different behavioral contexts. With response inhibition one is generally referring to a very specific motor response, such as pressing a key when a low tone sounds, but not pressing the key when a medium tone sounds. This requires one to suppress the motor response on medium-tone trials.
Avoidance is a more general and complex form of behavior than simple motor suppression. Avoidance refers to an organism consciously or unconsciously directing their behavior away from a particular stimulus or situation/environment (often a noxious or harmful stimulus/environment).
Although we could very loosely call both of these context-appropriate responses, they are vastly different kinds of behavior with different mental and behavioral processes involved in each.
AVOIDING is something that occurs in a framework and context known as "ESCAPE AND / OR AVOIDANCE" (the paradigm is who flees, escapes or avoids an unpleasant situation for him, instead of facing it: a subject avoids going to the dentist by deceiving himself by telling himself "I'll go" to never go or even, once in the waiting room of the Consultation, shortly after touching him, he leaves without further ado (escapes) ... with this, all he achieves is to increase his fear or phobia It is therefore a maladaptive mechanism - unless what is avoided is a real and objectively dangerous situation
INHIBIT, on the contrary, refers to a NORMALLY ADAPTIVE mechanism, so that inhibition or inhibitory control would be the ability of the human being to "repress" or control impulsive (or automatic) responses, and generate responses mediated by attention and reasoning (eg when faced with an aggressive or insulting comment from another, controlling one's expected aggressive response and keeping quiet or changing the subject); This requires superior cognitive control of "lower" emotions and impulses and requires maturity and adequate cognitive development that does not occur, for obvious reasons, in children, adolescents, demented states or Neurocognitive Disorder, intoxicated states or simply BAD EDUCATION ... for them, many people who define themselves as "UNINHIBITED" are simply immature or rude ... but, of course, up to a limit! since an EXCESSIVE INHIBITION would be typical of passive, repressed and / or fearful or social handicaps