Well, tbf, both trains and cars require converters

Totally! My idea was that -> arrows represent the converters and to put it simply more arrows = more efficiency loss. But right, since power can also be injected back into the network, which is a good thing, there could be <-> arrows, or maybe <=> to better hightlight the bi-directionality:

power lines <=> electric motor

Since you mentioned putting power back into the grid:

I heard another potential use for car batteries would be using them to balance out local power fluctuations in the grid to make it more stable. Since cars stand still most of their life anyway, they might as well be connected to the grid whenever they're parked. Not as a big energy reserve, since that wouldn't be very efficient and capacity would be too low, but just to keep things more balanced which is a healthy thing for the power network. I suppose that also applies for train batteries.