Key Inclusion Criteria:  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 Day 1, agreement to continue adequate contraception or abstinence through 3 months following the vaccination, and not currently breastfeeding. In Parts C and D, study participants must have been either previously enrolled in the mRNA-1273-P301 (COVE) study, must have received 2 doses of mRNA-1273 in that study, with their second dose at least 6 months prior to enrollment in this study (mRNA-1273-P205), and must be currently enrolled and compliant in that study (that is, has not withdrawn or discontinued early); or participant must have received 2 doses of mRNA-1273 under the Emergency Use Authorization (EUA) with their second dose at least 6 months prior to enrollment in mRNA-1273-P205, and able to provide proof of vaccination status at the time of screening (Day 1). In Part E, study participants must have previously received an mRNA vaccine for the prevention of COVID-19 in another clinical study or under EUA with their second dose at least 6 months prior to enrollment in mRNA-1273-P205 and must be able to provide proof of vaccination status at the time of screening (Day 1).  Key Exclusion Criteria:  Significant exposure to someone with SARS-CoV-2 infection or COVID-19 in the past 14 days, as defined by the US Centers for Disease Control and Prevention (CDC) as a close contact of someone who has had COVID-19. Known history of SARS-CoV-2 infection including during the mRNA 1273-P301 (COVE) study or within the last 18 months. Is acutely ill or febrile (temperature ≥38.0°Celsius/[100.4°Fahrenheit]) less than 72 hours prior to or at the Screening Visit (Day 0) or Day 1. 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 received systemic immunosuppressants or immune-modifying drugs for >14 days in total within 6 months prior to Screening (for corticosteroids ≥10 milligrams (mg)/day of prednisone equivalent) or is anticipating the need for immunosuppressive treatment at any time during participation in the study. Known or suspected allergy or history of anaphylaxis, urticaria, or other significant AR to the vaccine or its excipients. Has a medical history consistent with a protocol-specified AESI. Has received or plans to receive any licensed vaccine ≤28 days prior to the injection (Day 1) or a licensed vaccine within 28 days before or after they study injection, with the exception of influenza vaccines, which may be given 14 days before or after receipt of a study vaccine. Has received systemic immunoglobulins or blood products within 3 months prior to the Screening Visit (Day 0) or plans for receipt during the study. Has donated ≥450 milliliters (mL) of blood products within 28 days prior to the Screening Visit (Day 0) or plans to donate blood products during the study. Is currently experiencing an SAE in Study mRNA-1273-P301 (COVE) at the time of screening for this study.