No, these concepts are not the same. Passive immunity is a term used to describe the natural or artificial transfer of antibodies to an individual.
Herd immunity refers to how a population’s risk of a given disease decreases when the number of individuals immunised against that disease increases. For example, if the vast majority of a nation is immunised against measles, the infection has a difficult job spreading and infecting those who are not immunised. The herd immunity threshold varies according to the disease and how infectious it is. For measles, the estimated threshold is around 94%.