What this is called, and why the name matters
This has a name and a research literature, and there is a practical reason to know it. What helps in a relationship where two people fight badly is not what helps where one person is running a control project. Treating the two as one thing produces advice that gets people hurt.
What the research says
Stark E (2007). Coercive Control: How Men Entrap Women in Personal Life. Oxford University Press, New York
Stark's argument is that focusing on separate assaults misses the actual injury, which is liberty. Isolation, rules about daily life, monitoring and unpredictable consequence work together to remove a person's freedom of movement and judgement, and that removal is the harm, whether or not anyone is struck.
Johnson MP (1995). Patriarchal terrorism and common couple violence: two forms of violence against women. Journal of Marriage and the Family, 57(2), 283 to 294
Johnson separates violence that sits inside a project of control from conflict between two people that escalates without any control behind it. The two look similar on an incident form and are not the same thing, and what is safe to do about them differs completely. We have left the identifier off this line because we could not confirm it.
Postmus JL, Hoge GL, Breckenridge J, Sharp-Jeffs N, Chung D (2020). Economic abuse as an invisible form of domestic violence: a multicountry review. Trauma, Violence, and Abuse, 21(2), 261 to 283
Economic abuse is described in three recognised forms: restricting access to money, exploiting a person financially through debt or taken wages, and sabotaging their employment. The review's point is that it is not a milder category, because it is commonly the thing that removes the practical possibility of leaving. We have left the identifier off this line because we could not confirm it.