Transplant Recipients Key Inclusion Criteria  Is either a kidney or a liver transplant recipient who is at least 6 months post transplantation at the time of consent, and is either unvaccinated or previously vaccinated with 2 doses of Moderna COVID-19 vaccine who is at least 2 months after the second dose at the time of consent. Participants who received the 2 doses of Moderna COVID-19 vaccine before transplant are not eligible. Understands and agrees to comply with the study procedures and provides written informed consent. Is able to comply with study procedures based on the assessment of the investigator. Received chronic immunosuppressive therapy for the prevention of allograft rejection for a minimum of 6 months before signing consent, including but not limited to: glucocorticoids (such as, prednisolone), immunophilin binding agents (such as, calcineurin inhibitors, mTOR inhibitors), or inhibitors of de novo nucleotide synthesis (such as, mycophenolic acid, mizoribine, leflunomide, azathioprine). For female participants of childbearing potential: negative pregnancy test, adequate contraception or has abstained from all activities that could result in pregnancy for at least 28 days prior to the first injection, agreement to continue adequate contraception or abstinence through 3 months following the second dose (Day 29) for those receiving 2-dose regimen and, through 3 months following the third dose (Day 85) for those receiving 3-dose regimen, and through 3 months following the third dose (Day 1) for those previously vaccinated SOT participants, and not currently breastfeeding. Is medically stable, according to investigator's judgment, during the 3 months before signing consent.  Key Exclusion Criteria:  Has prior or planned administration of a coronavirus vaccine (for example, SARS-CoV-2 [for unvaccinated participants only], SARS-CoV, or MERS [Middle East Respiratory Syndrome] -CoV vaccine). Has current treatment with investigational agents for either prophylaxis against COVID-19 (for unvaccinated participants only) or treatment of COVID-19 (such as, anti-SARS-CoV-2 monoclonal antibodies). A history of more than one solid organ transplanted (such as, kidney and pancreas). A history of previous kidney or liver transplant is acceptable. Has received therapies that have depleting properties on T cells, B cells, and plasma cells (examples of depletional therapies include, but are not limited to, antithymocyte globulin [ATG], monoclonal antibodies, and proteosome inhibitors) within the last 6 months prior to enrollment. A history of biopsy-proven T-cell- or Ab-mediated rejection within 6 months of informed consent, or suspected active or chronic rejection according to the investigator's judgment. Has a known close contact with anyone with laboratory confirmed SARS-CoV-2 infection within 2 weeks to vaccine administration or known history of SARS-CoV-2 infection or positive SARS-CoV-2 test. Has a medical, psychiatric, or occupational condition that 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 history of clinically relevant donor-specific Ab according to the judgement of the investigator. Has a history of complications of immunosuppression Suspected clinically relevant active hepatitis, including viral hepatitis, according to the investigator's judgment Known human immunodeficiency virus (HIV) infection Has a history of a diagnosis or condition that, in the judgment of the investigator, may affect study endpoint assessment or compromise participant safety. Received any non-study vaccine within 28 days before or after any dose of vaccine (except for seasonal influenza vaccine, which is not permitted within 14 days before or after any dose of vaccine) Received intravenous blood products (red blood cells, platelets, immunoglobulins) within 3 months prior to Day 1. Participated in an interventional clinical study within 28 days prior to Day 0 or plans to donate blood products while participating in this study.  Healthy Participants  Key Inclusion Criteria :  In good general health without current or previous diagnosis of immunocompromising condition, immune-mediated disease, or other immunosuppressive condition, according to investigator assessment, at the time of consent, and has not been vaccinated with any COVID-19 vaccine at the time of consent. Understands and agrees to comply with the study procedures and provides written informed consent. Is able to comply with study procedures based on the assessment of the investigator. For female participants of childbearing potential: negative pregnancy test, adequate contraception or has abstained from all activities that could result in pregnancy for at least 28 days prior to the first injection, agreement to continue adequate contraception or abstinence through 3 months following the second injection, and not currently breastfeeding. Is medically stable, according to investigator's judgment, during the 3 months before signing consent.  Key Exclusion Criteria:  Has a known close contact with anyone with laboratory confirmed SARS-CoV-2 infection within 2 weeks to vaccine administration or known history of SARS-CoV-2 infection or positive SARS-CoV-2 test. Has prior or planned administration of a coronavirus vaccine (eg, SARS-CoV-2, SARS-CoV, or MERS-CoV vaccine). Has current treatment with investigational agents for either prophylaxis against COVID-19 or treatment of COVID-19 (eg, anti-SARS-CoV-2 monoclonal antibodies). Has a medical, psychiatric, or occupational condition that 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 history of a diagnosis or condition that, in the judgment of the investigator, may affect study endpoint assessment or compromise participant safety. Received any non-study vaccine within 28 days before or after any dose of vaccine (except for seasonal influenza vaccine, which is not permitted within 14 days before or after any dose of vaccine) Received intravenous blood products (red blood cells, platelets, immunoglobulins) within 3 months prior to Day 1. Received systemic immunosuppressants or immune-modifying drugs for >14 days in total within 6 months prior to Screening (for corticosteroids ≥20 mg/day of prednisone equivalent). Participated in an interventional clinical study within 28 days prior to Day 0 or plans to donate blood products while participating in this study.