The DS-2019 is the Certificate of Eligibility for Exchange Visitor (J-1) Status. It is issued by the exchange program's sponsor after it registers you in SEVIS, and it is the form you present at the visa interview and at the US border. For most IMG residents the sponsor is ECFMG, not the residency program.
The form lists your SEVIS ID, your program dates and the sponsor. Those dates matter: they set how long you may stay for training, and they must match what you tell the consular officer. A new DS-2019 is needed when training is extended or renewed, and the form should be kept safe and signed as the sponsor instructs.
The DS-2019 is not a visa. It lets you apply for one. See the J-1 visa process, and preparing for your visa interview. Your DS-2019 and visa also show whether you are subject to the two-year home residency requirement.