While there are occasional tensions between Singapore and Malaysia, Singaporeans and Malaysians travel across the causeway frequently. For Singaporeans, they usually travel to Johor Bahru for shopping. Due to the low cost of living and favorable Sing $ / Ringgit exchange rate, the purchases they make in Johor Bahru can often shave 50% of what they would have spent in Singapore.
In recent times, there has also been more cases of Singaporeans residing in Johor Bahru due to the favorable exchange rates.
Malaysians are not so fortunate. For premium shoppings and entertainment (Sentosa and Singapore Zoo for example), they have to fork out a substantial amount of Malaysian Ringgit, convert it to Singapore dollars which is less than half the numeric value of their Ringgit. There are continuing trend of students from Malaysia traveling into Singapore for study, so financially, they are also disadvantaged by the exchange rate.
Recent trend see Singapore Dollar (SGD) trading against the Malaysian Ringgit (MYR) at 1 SGD = 2.42 MYR. There has been a consistent appreciation of SGD against MYR, which explains why Malaysian Banks offer a higher interest rate compared to Singapore Banks.
For your information, a little about the history of Singapore Dollar and Malaysian Ringgit (from Wikipedia.org):
Between 1845 and 1939, Singapore used the Straits dollar. This was replaced by the Malayan dollar, and, from 1953, the Malaya and British Borneo dollar, which were issued by the Board of Commissioners of Currency, Malaya and British Borneo.
Singapore continued to use the common currency upon joining Malaysia in 1963 but, two years after Singapore's expulsion and independence from Malaysia in 1965, the monetary union between Malaysia, Singapore and Brunei broke down. Singapore established the Board of Commissioners of Currency, Singapore, on April 7, 1967 and issued its first coins and notes. Neverheless, the Singapore dollar was exchangeable at par with the Malaysian ringgit until 1973, and exchange with the Brunei dollar is still maintained.