Bahasa Melayu is a major language in Malaysia, Thailand, Singapore, Brunei, the Philippines and part of Indonesian island Sumatra.
The 7th century saw the birth of Old Malay in South Sumatra. Old Malay had a lot of loanwords from Sanskrit and was widely used as a trade language. After the 14th century, there were dialects emerging in Malaya, Jakarta and Ambon. During then, the language spoken on the islands of South Pacific was simplified Malay. The Standard Malay spoken in Malaysia is also called Malaysian, which is different from Indonesian in some basic vocabularies, pronunciation, certain tense and sentence structure.
Generally, the difference between Bahasa Malaysia and Bahasa Indonesia is a political concern, rather than a linguistic one. People speaking the two languages can communicate, though some vocabularies are used differently. What’s worth noting is that, people speaking different Malay dialects cannot easily communicate. For example, many Malaysian find it hard to understand the pronunciation of Kelantanese, and Javanese Malay has so many vocabs unique to its dialect that even Malaysian fluent in Bahasa Melayu cannot fully understand.
