Probably both if it ran dry and got hot, the smoke would be a bad sign.
Trans fluid is needed to cool the transmission, same as oil is used in an engine to cool the internal parts.
Heat kills automatics, which is why people add a second trans coolers to them.
The main pump in trans creates the pressure needed to circulate AFT and also to build up required pressure in the system.
When over heated the internal gaskets fail and pressure goes down, so gears can not engage.