Study to Evaluate the Safety, Reactogenicity, and Immunogenicity of mRNA-1403 and mRNA-1405 to Prevent Norovirus Acute Gastroenteritis in Healthy Adults 18 to 80 Years of Age

Key Inclusion Criteria: * Phase 1 Part: Adults 18 to 49 years of age at the time of consent or adults 60 to 80 years of age at the time of consent. * Phase 2 Part: Adults 18 to 80 years of age at the time of consent. * Body mass index of 18 to 39 kilogram/meter\^2 (inclusive) at the Screening Visit (relevant only for the base period of Phase 1 and Phase 2). * Participants assigned female at birth are eligible to participate if they are not pregnant or breast/chest/body feeding. * A person of childbearing potential is using a highly effective contraceptive method. * Participant has provided written informed consent for participation in this study. Key Exclusion Criteria: * Is acutely ill or febrile (temperature ≥38.0°C \[100.4°F\]) 72 hours prior to or at the Screening Visit or Day 1. * Phase 2 Part booster extension period: acute disease or febrile 72 hours prior to or on Day 365. * History of a diagnosis or condition that, in the judgment of the Investigator, is clinically unstable or may affect participant safety, assessment of safety endpoints, assessment of immune response, or adherence to study procedures. * Has a medical, psychiatric, or occupational condition, including reported history of substance abuse, which may pose additional risk as a result of participation, or that could interfere with safety assessments or interpretation of results according to the Investigator's judgment. * Has a current or previous diagnosis of immunosuppressive condition, to include human immunodeficiency virus, or immune-mediated (autoimmune) disease that requires immunosuppressive therapies. (drugs or biologics). The use of topical corticosteroids or other immunosuppressive agents (for example, topical calcineurin inhibitor) may be eligible for participation at the discretion of the Investigator. * History of anaphylaxis, urticaria, or other significant AR requiring medical intervention after receipt of a vaccine or intervention that includes one or more of the same components contained in the study vaccine. * Phase 1 Part and Phase 2 Part base period: Any history of myocarditis or pericarditis. * Phase 2 Part booster extension period: Any history of myocarditis, pericarditis, or Guillain-Barré Syndrome. * Coagulopathy or bleeding disorder considered a contraindication to IM injection or phlebotomy. * Dermatologic conditions that could affect local solicited AR assessments (for example, tattoos, psoriasis patches affecting skin over the deltoid areas). * Has received systemic immunosuppressive therapies (drugs or biologics) for \>14 days in total within 6 months prior to Screening or Day 365 (Phase 2 Part booster extension period only) (for corticosteroids ≥10 mg/day of prednisone equivalent) or is anticipating the need for immunosuppressive treatment at any time during participation in the study. Inhaled, nasal, intra-articular, and topical steroids are allowed. * Has received or plans to receive any licensed/authorized vaccine (to include severe acute respiratory syndrome-related coronavirus-2 vaccine) ≤28 days prior to or within 28 days after each study intervention, with the exception of influenza vaccines, which may be given 14 days before or after receipt of a study intervention. * Has received systemic immunoglobulins or blood products within 3 months prior to Screening or Day 365 (Phase 2 Part booster extension period only) or plans for receipt during the study. * Has donated protocol-specified volume of blood products within protocol-specified timeframe. * Participated or plans to participate in an interventional clinical study within protocol-specified timeframe. * Phase 2 Part: Individuals who are participating/have participated in the Phase 1 part of the study are excluded. * Phase 1 Part: Any individual with laboratory abnormalities achieving thresholds defined in the protocol.