To travel from Moldova to Romania by train, buy your tickets at a railway station. There are no online tickets available.
From Chisinau there is a direct night train via Iasi to Bucharest. Additionally there are local trains from Ungheni across the border to Iasi with connections from Chisinau.
To travel from Moldova to Russia by train, buy your train ticket via one of the given booking links or locally at a train station in Moldova.
There are daily overnight trains available from Chisinau (Moldova) via Ukraine to Moscow (Russia).
If you want to travel from Moldova to Ukraine by train, buy your ticket at a train station. There are direct trains from Chisinau to Odessa and Kyiv.