Do you understand how the immune system works?
A simple explanation would be to say it works on complementary shapes.
Vaccinations use heat killed pathogen or antigens or other surface markers on antigens called epitopes, attenuated pathogen, recombinant derived pathogen or epiptopes, a benign version of a closely related species such as cow pox/small pox.
Vaccinations often contain adjuvants that heighten the immune response.
Once the immune system is challenged by a pathogen or foreign substance it undergoes a process of clonal selection. The relevant B or T cells are coopted and multiply to produce a magnified response. This is the same whether the pathogen or foreign substance has been introduced naturally or artificially.
Since the immune response is going to function in the same way whether an antigen has been introduced naturally or artificially then the collective efficacy will be the same = herd immunity.
