Hi, Pearl,
There are lots of behaviors that could be considered abusive, but one sure sign is if the behavior is something for which you could get a restraining order. When the law recognizes it as abuse (or domestic violence) then you can feel pretty confident that it is.
Throwing and breaking things, and sending many, many texts and phone calls, are legally defined as harassment most places, and would be grounds for criminal charges and/or a restraining order. Subtler things, such as constant put-downs or insults are emotionally abusive even though the law might not treat it as harshly. It can certainly be very damaging to the person on the receiving end, with malicious intent, so I think it would qualify as abuse for purposes of recognizing the behavior as such.
Why do you ask? Are you considering a restraining order?