As you know, there are three pairs of trains running between India and Bangladesh: The Bandhan Express between Kolkata and Khulna, the Maitree Express between Kolkata and Dhaka Cantt, and the Mitali Express between New Jalpaiguri and Dhaka Cantt.
Of these, only the Bandhan Express has an exact counterpart from before Partition. This was known as the Barisal Express which ran between Sealdah and Khulna. The railway has not reached Barisal (now Barishal) yet, though this may happen in the near future.
The Barisal Express of 1944 is covered here;
That was running between 2017 and 2020, and has restarted in 2022. The main details are here:
Note that the rake has 4 AC-1 and 4 AC chair coaches and no other passenger coaches. In general, Indian rakes and Bangladeshi rakes are used on alternate days.
An IR diesel (normally a Howrah WDM-3D) hauls the train between Kolkata and Benapole, which is about 2 km beyond the border. A BR diesel (normally an Ishurdi WDM-3A) takes it onward to Khulna. The track is electrified up to Bangaon, so an electric loco could have been used up to there.
The timetables showing all intermediate stations:
Note the stoppages at Petrapole, Benapol and Jessore
The stoppages are the same.
A few pictures of stations on the Bangladesh side:
Joshore (Jessore) Jn
It can be seen that even in large stations, most boards may be only in Bangla.