I have been accused of abuse on multiple occasions with my current relationship by people who outside of it. The accusation is baseless and ridiculous on its face. There are many differences between a healthy BDSM relationship (any healthy relationship, really) and an abusive relationship. The differences are not difficult to spot, but I will spell them out for people who don't understand BDSM and need to know how things work.
One mark of abusive relationship is the isolation of the victim from friends, family, and work in order to control that person's every move. Allowing a victim his or her own money makes it easier for that person to leave. Keeping him or her away from friends and family makes it difficult to flee to a sympathetic person's home to get away from the abuse. The abuser might take away the victim's means of transportation, as well.
I do not isolate my slave at all. It is in our contract for her to maintain ties with her family, and she does. She maintains contact with her family members, and she has time for her kids. She has her own vehicle. I don't take her money from her.
The abuser will administer the abuse, whether physical or psychological, and later apologize, be charming as can be, and soothe the victim. It's a bit like aftercare, really; the abuse is traumatic, and the false remorse smooths it over in a lot of cases.
I make no apologies for what I do with my slave. The pain I cause and the names I call her are what we both wanted from the beginning. I never have to apologize for our BDSM activities, because I've done nothing without her consent.
Lack of consent
The abuse victim never consents to the abuse. There is no safe word or phrase to get out of the abuse. It happens whether the victim wants it to or not.
BDSM is all about consent, when it's healthy, and I obtained my slave's full, explicit, written, un-coerced consent in the beginning of our relationship. How many people can say that they've done so in their own relationships? That consent does not remain implied; if the play goes too far for her for whatever reason, she can stop it with a safe word. Actually, she has more than one, and she has safe actions, as well. Her consent ends when she says her safe phrase.
The abuser will often threaten the victim with harm to him/her or any children they might have, or to the family of the victim, if the victim threatens to leave.
I would never make such a threat. If she wanted to leave, I'd want to understand why, but I wouldn't threaten her, her children, or any other family member with harm for that decision. The contract is not legally binding. It means something to us--it means a lot to us--but it's not a legal contract. You can't own a person. It does give evidence of consent--as if I'd ever need it.
The abuser will show one face in private, but another face when with other people aside from the victim. The victim can never visit family or friends alone. That would give the victim opportunity to talk about the abuse and make a plan to get away.
My slave is always free to visit family by herself, and if she wanted to go to a friend's, she could. She is free to take her children out without me. I love spending time with her, but sometimes, with my work schedule or whatever reason, it's not practical. Sometimes, she just wants to do something special, one-on-one, with one of her children.
Diminishing the victim's self-worth/self-image
The abuser will tell the victim he/she is not good/pretty/smart enough to be with anyone else. The abuser will make the abused feel worthless. Sometimes, the abused will do anything to win the approval of the abuser, thinking the abuse is somehow his/her fault. If only he or she could do better, the abuser wouldn't inflict physical and/or emotional pain. The abuser will never accept anything as good enough.
While humiliation and degradation are parts of BDSM play at times, I never make my slave feel like she's worthless. She's my precious treasure. She's beautiful, and I tell her so. She's sexy, and I tell her that. She cooks wonderful meals, and I thank her and praise her for it. She makes me happy in so many ways, and she knows it.
If you're being abused, get away as soon as you can!
Anyone who does anything without your consent is abusing you. You do not deserve to be abused, and the abuse is not your fault. You should get out of the relationship as soon as possible. There are shelters for victims of abuse in many places, in many countries. You don't have to remain a victim.
The biggest tragedy of abuse cases is that there isn't as much help for it as there should be. Abuse victims often have to start from nothing. There are resources, but the stories I've heard from victims who have used these resources have grim tales to tell. Your safest bet is to recognize the red flags early and get out before the relationship gets serious. As soon as any attempt at isolation happens, get away. As soon as the abuser does something without consent, get away, As soon as the person wants you to quit your job or tries to control your money, get away. Always maintain your ties with family and friends, and if the abuser tries to keep you from doing that, get away.
It's never simple. I know. I've heard too many stories to be naive about it. Just remember that it's not your fault you've been abused. Some abusers are quite good at what they do. You've been manipulated by someone who is better than most people at manipulation. Don't be hard on yourself. Your life is worth it. Your children, if you have any, are worth it.
Last bit of advice: document everything! If you can see a therapist, do it--that's documentation you can use later. If you have kids, get them into therapy, too. It will help later.