There is much debate about whether Moldovan is a dialect of Romanian, or a separate language. As far as linguists are concerned, Moldovan and Romanian are the same, or are closely-related, mutually intelligible dialects of the same language. According to Wikipedia, Moldovan is the official name for the Romanian language in the Republic of Moldova and in the territory of Transnistria. About 2.6 million people speak this language/dialect in Moldova.
Until 1989, Moldovan was written with the Cyrillic alphabet. After that the Romanian version of the Latin alphabet was adopted in Moldova, though some orthographic changes adopted in Romanian are not generally used in Moldova. In Transnistria the Cyrillic alphabet is still used.