The correct answer is both are branches of acquired immunity.
The adaptive immune system or the acquired immune system includes both the components which are the humoral immunity and the cell mediated immunity.
The acquired or adaptive immune system creates an immunological memory after it encounters an initial response to a specific pathogen which leads to enhanced response to the following encounters with that same pathogen. This adaptive or acquired immunity forms the basis of the process of vaccination. The acquired immunity is specific to a high extent against the particular pathogens.