Love addiction is closer to "romance addiction" - addicted to "being in love, being in a romantic relationship."
Codependency does not have to involve romance at all. Parents can be codependent and try to bail out their kids over and over again. Or you have one brother who is continuously saving the other one who is getting in trouble, being pulled down at the same time. Or even you could say that codependents are individuals who grew up in a dysfunctional environment and are applying the same dysfunctional coping skills in their adult life.
Also codependency may include love addiction, when being "in love," being in a relationships is a must, regardless of consequences.