ACC Shewan, the national policing lead on restorative justice, had said that in some rare cases it might be appropriate to deal with domestic abuse out of court via community resolutions.
He used the hypothetical example of a jilted boyfriend who had never been violent before but who, upset and angry, snaps off his ex-girlfriend's car wing mirror after being dumped.
Speaking on BBC Radio 4's Today programme, he said: "That is domestic abuse."
But he added that in a case like this the victim might merely want her ex-partner to pay for the damage, not for the case to end up in court.
ACC Shewan stressed that only a small number of cases were being dealt with in this way. In a statement, Ms Baird, the PCC for Northumbria, condemned his remarks.
She said: "Those who suffer from domestic abuse are not always victims of violence every time.
"Sometimes they are coerced and oppressed by relatively minor conduct. Officers in Northumbria understand that they can be in the context of continuing abuse and do not trivialise it as this officer (ACC Shewan) seems to do.
"Victims need to have confidence in the system and know that they have the full weight of the law behind them."
Ms Baird was not available to comment further as this article went live.
'Indistinguishable'Asked to clarify whether Ms Baird differentiated between domestic violence and domestic abuse, her press spokeswoman Ruth Durham said: "Abuse is violence. They are both unsuitable for community resolutions and restorative justice."
Asked whether Ms Baird believed that shouting at someone was as bad as punching a person in the face, she added: "Her position is that domestic abuse is the same as domestic violence."
Shadow Home Secretary Yvette Cooper has said that police are too often dealing with cases of domestic violence by way of community resolutions, which could amount to little more than a "slap on the wrist".
However, by refusing to acknowledge any difference in degree between cases, Ms Baird, a former Labour MP, has gone further than others in her party.
PoliceOracle.com recently highlighted the case of a 16-year-old boy given a caution for criminal damage and domestic violence after dropping a jar of pickles in his home.
Chris Bath from the National Appropriate Adult Network said this demonstrated how trivial incidents could sometimes be termed as violence by police when in fact this was not an accurate description of the incident.
Frances Crook, Chief Executive of the Howard League for Penal Reform, has defended ACC Shewan's stance, saying the police had "got it about right by using their discretion".
She told PoliceOracle.com: "If it is a minor altercation, using some kind of community resolution is best for everybody."
Ms Crook said there was a need to distinguish between domestic violence and domestic abuse.
The latter could be relatively minor, she said, for example Facebook harassment.
Victims' voicesMs Baird's fellow PCCs have also stopped short of conflating domestic violence and domestic abuse.
Tony Lloyd, a Labour politician and the PCC for Greater Manchester, has called for domestic violence to be made a specific offence to acknowledge its seriousness and make it distinct from other offences.
Several PCCs are researching how police treat victims of domestic violence and domestic abuse in an effort to provide better support for them.
Suffolk's PCC Tim Passmore is working with academics from University Campus Suffolk to understand victims' experiences through the criminal justice process.
The Labour Party has pledged to introduce a Violence Against Women and Girls Bill "to place