Is it permissible to continue giving zakat to a widow who was eligible for it, but then acquired an income? And is that considered zakat or sadaqah?

If a woman's salary is insufficient for her and her children to cover their essential needs, then she is poor or needy, and it is permissible to give her zakat. However, if her salary is sufficient for her and her children, then she is not considered among those eligible to receive zakat, and it is permissible to give her voluntary charity.