Regarding the languages of Malaysia, it can be said that Malay has both broad and narrow meanings. In a broad sense, Malay refers to the languages of the Indonesian branch of the Austronesian language family; in a narrow sense, it refers to a language used in countries near the Strait of Malacca. The narrow sense of Malay (Bahasa Melayu) belongs to the Indonesian branch of the Austronesian language family in terms of linguistic classification.
The number of people worldwide who use Malay ranges from 7 million to 18 million, primarily used in Malaysia and its neighboring countries, such as Thailand, Singapore, Brunei, and parts of Sumatra, Indonesia. Before 1945, Malay was also used in many places outside of Sumatra, Indonesia. However, after Indonesia declared independence from the Netherlands that year, the Malay used in that country became known as Indonesian (Bahasa Indonesia). In addition, Malay is also a widely used working language in East Timor.
In Malaysia, approximately 13 million people speak Malay as their native language, accounting for about 52% of the national population. Furthermore, there are 10 million people in Malaysia who use Malay as their second language. As for other countries, there are 10 million Malay speakers in Sumatra, Indonesia, 1 million in Thailand, and about 400,000 in Singapore (Ethnologue: Languages of the World 2017; Bowen Translation Co., Ltd. n.d.).
According to a tacit understanding reached by Malaysia, Indonesia, and Brunei, Malay uses the Riau dialect (Bahasa Riau) — the dialect of the Riau province in Sumatra — as its standard form. This is because the Riau province, now part of Indonesia, has long been considered the birthplace of the Malay language.
In Malaysia, Malay is referred to as "Bahasa Melayu (Malay language)" or "Bahasa Malaysia (Malaysian language)." "Malaysian language" was a term used by the Malaysian government in the 1967 "National Language Act." Until 1990, "Malaysian language" was a name more commonly used to refer to Malay. However, after 1990, both government officials and scholars in academia have increasingly tended to use "Malay language" — the term used in the Malay version of the "Federal Constitution of Malaysia" — to refer to the language.
After declaring independence, Indonesia also used a form of Malay as its official language, but referred to it as "Bahasa Indonesia (Indonesian language)." As for Brunei and Singapore, the Malay they use is simply called "Malay" or "Bahasa Melayu (Malay language)."
Basically, the distinction between "Malay language" and "Indonesian language" is based on political reasons rather than linguistic considerations. People who use these two languages can basically communicate with each other, although many vocabularies are not exactly the same. However, it is worth noting that many Malay dialects are not fully mutually intelligible. For example, for many Malays, it is difficult to understand the pronunciation of Kelantanese. In addition, Javanese Malay has many unique vocabularies that even Malays familiar with the Malay language cannot fully understand.
The difference between Malay and Indonesian can be compared to the difference between British English and American English. People who use these two languages can basically communicate with each other, with only some differences in the spelling of the writing system and vocabulary. The main reason for this difference is that Indonesian has borrowed many words from Javanese and Dutch.