Map of the Malay peninsula showing the Straits Settlements in red, the Federated Malay States in yellow and the Unfederated Malay States in blue:

The East India Company controlled Penang, Malacca and Singapore from 1824 to 1867, after which it became a crown colony known as Straits Settlements. The remaining Malay states were protectorates, of which a few federated in 1895. In 1909 the Anglo-Siamese Treaty forced Siam to cede its southern provinces to the British, forming the current Thai-Malaysian border.
Diagram of the geopolitical history of Malaysia, Singapore and Brunei:

In 1948 the Federation of Malaysia was founded including British North Borneo and Sarawak. Singapore was expelled in 1967 forming the current situation.
Currency
Before 1825 Spanish Dollars formed the main silver currency, which was worth 400 Keping (copper coin) or 4000 Pitis (a tiny tin coin). Penang used Dollars subdivided in 100 Cents which were also named Pice. In 1825 Sterling was made the official currency of the entire British Empire, but it never became widely used in East Asia. Instead, the Straits Settlements, controlled by the East India Company, introduced the Rupee in 1837 at a rate of 48 Pice/Cents per Rupee.
Spanish Dollars remained popular in the area and the introduction of the Hong Kong Dollar made the Straits Settlements adopt this too around 1870 at a rate of around 2.5 Rupees.
As of March 2016, all EIC coinage listed under Malay Peninsula and under Netherlands East Indies haave been moved to British East Indies.
Coins
Tin coins denominated in Pitis and copper or bronze Keping coins were struck for various settlements and states. Penang, the capital of the Straits Settlements before Singapore took that role issued coins in Cents and fractions of Dollars. The Malacca coin of 1 Keping is known as the 'Haantjesduit' (Cock Duit) in the Netherlands as it circulated next to Dutch East India Company (VOC) money.
https://en.numista.com/catalogue/peninsule_malaise-1.html
Coins of British East Indies:
https://en.numista.com/catalogue/british-east-indies-1.html