In case of India:
From 1773 to 1858, the British administrative head in India was called Governor General and was selected by the Court of Directors of the East India Company, to whom he was responsible.
After the 1857 Uprising, the government of India was transferred from the East India Company to the Crown.
And "Viceroy" was added to the title of the Governor General and was called as a Viceroy Of India.
Viceroy was appointed by the sovereign on the advice of the British government; the Secretary of State for India, a member of the UK Cabinet, was responsible for instructing him on the exercise of his powers.
After 1858, Viceroy Of India , as a Viceroy, direct representative of the Crown, dealt with the princely states of India, whose relationship was not with the British government, but directly with the monarch. And as a Governor General, govern the British India provinces.
Generally, if there is a dominion status, the administrative head is called only as a Governor General. For example, after India's independence on 15th Aug. 1947, till the India become republic in 1950, she had a dominion status. And in this period, Lord Mountbatten was made Governor General. He remained till 1948 and after him C. Rajagopalachari become the Governor General. The other dominions (Canada, Australia, etc) too have a post named only as a Governor General.