The Dutch got both Run and Suriname, while the English got Manhattan. However, it wasn’t exactly a matter of saying, ‘you give me Manhattan and I give you Suriname and Run.’ What happened was that, in the Peace of Breda that ended the Second Anglo Dutch War in 1667, it was agreed that Dutch and English got to keep whatever they had taken by May 20, 1667.

For the English, they had taken control of New Amsterdam, the fort at the southern tip of what is now Manhattan, in 1664 (in fact, before the outbreak of the Second Anglo Dutch War).

For the Dutch, they had captured Surinam on 6 March 1667.

The situation in Run was a bit more complicated.

As early as 1621 the Dutch had invaded the main Banda Island and practically depopulated it, slaughtering an estimated 13,000 Bandanese. They then moved on to Run and demanded its surrender. The terrified Bandanese, including refugees from Banda Island, surrendered.

This left the English fort on Nailaka, a tiny island to the northeast of Run, the only English presence on the Banda Islands. In 1623, the East India Company and VOC agreed that the East India Company could have Run back, but the East India Company never made any practical moves to take it over as it lacked the means to effectively occupy and govern it. Thus, the Dutch were able to destroy all nutmeg trees on Run, which made it even less attractive to the English. The English never turned their theoretical control over Run into reality.

In 1666, when news of the Second Anglo Dutch war reached the Banda Islands, the Dutch on Banda sent troops to occupy Run. The English commander of the fort at Nailaka surrendered the garrison in return for safe passage. Thus, the Dutch were able to take ‘real’ control of Run, Nailaka and thus the entirety of the Banda Islands in 1666.

As the above three conquests were completed before May 20, 1667, they remained in the hands of whoever was the last to have conquered them. Although England and the Netherlands would go on to fight the Third Anglo Dutch War, and I think Suriname at least changed hands a couple more times, the Treaty of Westminster in 1674 ‘rolled back’ the status of the above three territories to whatever they had been in the Peace of Breda and they remained that way until they were lost in one way or another.

Loth V. C. (1995) Armed Incidents and Unpaid Bills: Anglo-Dutch Rivalry in the Banda Islands in the Seventeenth Century. Modern Asian Studies 29(4) pp. 705-74