Same and different. Immunotherapy is a medical term defined as the treatment of disease by inducing, enhancing, or suppressing an immune response. Some are designed to elicit or amplify an immune response and are called activation immunotherapies. Vaccines are of this type. While immunotherapies that reduce or suppress are classified as suppression immunotherapies.
Immunity. They are fundamentally similar in that you are providing the stimulus (either infectious or allergenic) into the body triggering an immune response to provide a certain level of protection. Allergy shots just take longer to develop this immunity.