Apparently, Papua is the original name for the whole island which the natives used. New Guinea was a term used by the Spanish explorers, and picked up by the Dutch when they colonised the western half in the 17th century.
Ok, here's the somewhat fascinating timeline.
February 1883 Report in the Sydney Morning Herald on February 7, 1883 summarizing the first part of a report in the Allgemeine Zeitung — a leading political daily journal published in Munich, Germany — back on November 27, 1882.
Under the heading German annexation of New Guinea … the explorations of Powell, Moresby, Macfarlane, etc have made the island now worth some consideration. It is considered useful by geological and biological people as holding in its forests the key to solve problems - by London missionaries as a field to win new souls - by better informed colonial politicians of all nations as a profitable field for cultivation.; therefore geographical inquiries about it are now little likely to come to a standstill. As we Germans have learnt a little about conducting colonial policy, and as our wishes and plans turn with a certain vivacity towards New Guinea … according to our opinion it might be possible to create out of the island a German Java, a great trade and plantation colony, which would form a stately foundation stone for a German colonial kingdom of the future."
March 1883 Following cries for help, particularly from missionary organizations, Queensland Premier McIlwraith on his own authority ordered a Queensland Police Magistrate to proclaim the annexation on behalf of the Queensland government of New Guinea east of the Dutch boundary. When news of this reached London, the Secretary of State for the Colonies, Lord Derby promptly repudiated the act. When the matter came before Parliament, Lord Derby advised that the British Imperial Government "were not ready to annex New Guinea in view of its vast size and unknown interior, the certainty of native objections and administrative expense"
May 1884 Adolph von Hansemann, who became one of the richest men in the German empire, worked with a syndicate of German bankers to form the New Guinea Consortium.
3rd November 1884 Under the auspices of this Deutsche Neuguinea-Compagnie (New Guinea Company), the German flag was flown over Kaiser-Wilhelmsland (not far from Bougainville), over the Bismarck Archipelago, and the German Solomon Islands. The whole area became known as German New Guinea.
6th November 1884 Three days later, after the Australian colonies promised financial support, the territory of New Guinea (in the south) became a British protectorate. Peter Scratchley, back in 1860 appointed as defence adviser for Australia by the Colonial Office, and who had built Fort Lytton in Brisbane in 1880, although he had previously retired in late 1882, now became special commissioner for New Guinea.
1885 in the north. Arrival of first German Missionaries. German church authorities devised a definite program for missionary work in New Guinea and assigned it to the Rhenish Mission, under the direction of Friedrich Fabri (1824 91), a Lutheran. The missionaries faced extraordinary difficulties: repeated sickness from the unhealthy climate; psychological and sometimes violent tensions and fights between the colonial administration and the natives. The natives rejected European customs and norms of social behavior; few embraced Christianity. In 1921 the Rhenish Mission pulled out, handing the territory over to the United Evangelical Lutheran Church of Australia.
Note, efforts sponsored by the Catholic Church in Germany were allegedly more successful. They put more emphasis on tradition and less on modernization, and were more in line with native world-views and traditions, European morality and discipline were often adopted, as were notions of dignity and prestige.
1885 in the south. Arrival of Special Commissioner Peter Scratchley. Back to 1885. In August, Peter Scratchley arrived in Port Moresby. Made it the seat of government, questions of land tenure and the cultivation of the land were examined, and good relations were established with many of the natives and with the missionaries. However, died of malaria shortly after arriving, in December 1885.
1888 After a few temporary commissioners, British New Guinea (in the south) was formally annexed to Great Britain. A Scotsman, William MacGregor, a chief medical officer in Fiji for many years, was appointed as formal administrator. Served there for ten years. Click here for a list of his successors.
1899 Forced recruitment in the north. Meanwhile, in order to expand the highly profitable plantations, the German Imperial Government now administered New Guinea in the north through a Governor, who was assisted after 1904 by a nominated Government Council. Military expeditions were sent to take direct control of more areas, and instead of voluntary recruitment it became a matter of forced mobilization. New laws were enforced that required the tribes to furnish four weeks of labor per person annually and payment of a poll tax in cash, thereby forcing reluctant natives into the work force. The government did explore the choice of voluntary recruitment of laborers from China, Japan, and Micronesia, but only a few hundred came. After 1910 the government tried to ameliorate the impact by ending the recruitment of women in some areas and entirely closing other areas to recruiting. The planters protested vehemently, and the government responded by sending troops to fresh areas to impose the labor policy.
1906. Back to the south, British New Guinea placed under Australian administration. On September 3 control of British New Guinea was transferred to newly federated Australia, and renamed as Papua.
1914 First World War. After some brief fighting, on 21 September 1914 all German forces in the colony surrendered to Australian troops.
1919 Treaty of Versailles. Germany lost all colonial possessions including this German New Guinea. It became the Territory of New Guinea (as opposed to Papua), a League of Nations Mandate Territory under Australian administration.
1942 War in the South Pacific and planned invasion of Port Moresby. In January Japan captured Rabaul on New Britain island. On 8 May, in the Battle of the Coral Sea, both sides (i.e. US and Japan) located and attacked the other's fleet carriers, with both sides suffering heavy aircraft losses and carriers sunk/damaged. With the loss of carrier air cover the invasion of Port Moresby by sea was called off.
In July the villages of Buna and Gona on the north side of the Kokoda Trail leading to Port Moresby (in the south) were captured by Japan. In August, fortuitously, the US invasion of Japanese held Guadalcanal in the South Solomon Islands was of great assistance to Australia late September defence, as the US ongoing success in holding Guadalcanal was just enough to give Japanese authorities pause to their army making an imminent Port Moresby attack; they came within 30 kms. Click here for further details and the Run Rabbit issue.
1943-44 Japan driven back to Wewak and Rabaul.
1945 On 13 September Japanese troops in Wewak and Rabaul surrendered. Plans made for Papua New Guinea to be administered by Australia as a single territory.
1949 Territory of New Guinea was formally merged with the Australian territory of Papua, becoming the Territory of Papua and New Guinea.
1951-1975 The 1949 act provided for a partly elected Legislative Council (established in 1951), a judicial organization, a public service, and a system of local government. A more fully elected House of Assembly opened 8 June 1964. Australia invited the World Bank to send a mission to the Territory to advise on measures regarding economic development and political preparation. In 1972 the word "Territory" was removed and the country became Papua New Guinea. Elections that year resulted in the formation of a ministry headed by Chief Minister Michael Somare, who pledged to lead the country to self-government and independence. Papua New Guinea became self-governing on 1 December 1973, then independent on 16 September 1975.
1974 First documented record of Tok Pisin, ("Talk Pidgin") the Creole language widely used throughout the country.
1975-2015 Click here for a recent article written in 2015 on its early independence under Michael Somare (1975-2011), and Peter O'Neill (2011-2019), that included the civil war in Bouganville (1989-1998).