Map of Moldova with Transnistria to its east. The government of Moldova regards Transnistria as an autonomous region within its own borders, but has no control over the area. The Transnistrian authorities regard the territory as an independent republic, but it has very limited international recognition.
Moldova's history traces back to Roman times, when the region was on the outskirts of the Roman Empire. In 1359 the Principality of Moldavia was established, which became a semi-independent Ottoman vassal in 1538. In 1600 a short-lived union between Moldavia, Transylvania and Wallachia existed as the first Romanian Kingdom, but it was conquered by the Polish-Lithuanian Commonwealth a year after.
The first Romanian Kingdom of 1600-1. Moldavia is located on both sides of the Prut river.
In 1621 Moldavia became an Ottoman vassal again. The Russian Empire occupied both Moldavia & Wallachia during the Russo-Turkish War of 1770-4, but returned them as Ottoman vassals. Transnistria was eventually annexed in 1792 and 1793, and eastern Moldavia in 1812, which established the same border on the Prut river that exists today between Romania and Moldova.
Western Moldavia and Wallachia became united provinces in 1859, and formed the basis of an independent Kingdom of Romania that emerged fully in 1878 as the result of another Russian victory over the Ottoman Empire. The Romanians fought this war on the Russian side, and in return Romania gave up its claim on eastern Moldavia.
During WW1 Romania sided with the Central Powers and conquered present-day Moldova from what was left of the Russian Empire in 1918.
Romania after WW1, when it annexed Transylvania from Hungary, Bukovina (Cernauţi area) from Austria and Moldova (Bessarabia) from Russia.
In the 19th century the demographics of Transnistria had changed due to Russian and Ukrainian immigration. It stayed within the USSR as the Moldavian ASSR, with Moldavians a large minority of around 40%.
In 1940 the USSR demanded Moldova (named Bessarabia in those days) from Romania, which surrendered it without a fight. In 1941 Romania sided with Nazi Germany and Hungary to attack the Soviet Union. Romania annexed not only Bessarabia but was also awarded vast parts of land east of the Dniestr river, including the Black Sea harbour city of Odessa. Romanian and Moldavian soldiers reined with terror, with 250,000 casualties as a result during the 3 years of occupation. In 1944 the Red Army restored the border of 1940 (and of 1812-1918) and established the Moldovan SSR out of Bessarabia (but moved the south part to Ukraine) and Transnistria.
During the 1980's nationalist movements gained popularity in the USSR, with the Popular Moldavian Front (PMF) claiming power in Moldova. Independence was proclaimed in 1990, and the PMF became more and more aggressive towards non-Moldavians. The Russian and Ukrainian inhabitants of Transnistria felt threatened and wished to preserve the Soviet Union. When organised mobs started to wreak havoc in Transnistria the Soviet Army which was still stationed there intervened, ending the War of Transnistria of 1992.
Ever since Moldova has been a split country (if you follow internationally recognised borders). The Transnistrian situation is often referred to as a frozen conflict. Periods of thaw are followed by periods of provocations. A peace deal was almost concluded in 2005, but was ultimately rejected by Moldova which did not accept the terms of autonomy for Transnistria.
Moldova is one of the poorest countries in Europe. Before the breakup, Transnistria formed 60% of the Moldovan SSR's economy. Moldova had to transition from mostly agriculture to services, and its growth numbers have been quite steady since 2000.
Currency
After indepence, Moldova replaced the Soviet Ruble with the Moldovan Cupon at par in 1992. Hyperinflation caused the Cupon to be replaced by the Leu at a rate of 1000 to 1 in 1993. In 1996 there were 4.5 Lei in a US Dollar. The currency gradually fell to 13/$ in 2006 and 20/$ in 2016.
Coins
The Principality of Moldavia had its own coins in the 14th and 15th century, based on the Grosh, Denar and Ban. Due to the fact that the region had no access to silver mines supply came mostly from foreign coins, and local coins disappeared. The most popular silver coin became the Dutch/Flemish Leeuwendaalder, a larger silver coin. The name of the Leu is derived from this coin.
During the Russo-Turkish War of 1770-4, both Moldavia and Wallachia were occupied by the Russian Empire. Coins were struck for the Principalities during this era, using legends in Cyrillic script. The monetary system tried to unify the Ottoman Para with the Russian Kopek, at a rate of 2 Para = 3 Kopeks.
Moldova's first modern coins appeared in 1993, with 1 Ban to 50 Bani in aluminium and 1 and 5 Lei in steel. The latter two were withdrawn from circulation quite quickly and replaced by banknotes. The 1 and 5 Lei coins are therefore somewhat hard to find. In 1997 an aluminium-bronze 50 Bani replaced the aluminium version. A new series of 1, 2, 5 and 10 Lei were added in 2018.
Transnistria uses a separate currency, which is the Transnistrian Ruble. It was introduced in 1992 at par with the Soviet Ruble and revalued in 1994 and 2000. In 2000 the first Transnistrian coins appeared. The Soviet emblem is depicted on the coins with the name Pridniestrovye Moldavskaya Respublika, or 'Moldavian Republic by the Dniestr'. In 2015 non-metal 'coins' made of composite with values 1, 3, 5 and 10 Rubles were added. A US Dollar bought 11 Transnistrian Rubles in 2014.
Coins of modern Moldova:
https://en.numista.com/catalogue/moldavie-1.html
Coins of Transnistria:
https://en.numista.com/catalogue/transnistrie-1.html
Coins of Moldavia & Wallachia:
https://en.numista.com/catalogue/moldavie_valachie-1.html
We have a new referee there. 
But we still have only one coin from those duchies. 
I believe this can wait a little. But as a prospect to future, yes, they could be splitted. 