From a native speaker of American English: it would much more natural to say, "the children run onto the airplane".
Here, "running into" sounds exactly like the children are crashing with the plane
Strictly logical speaking, into is a movement where something/-one gets inside of something. And i think usually not right through anything solid but via openings.
Run onto, on the other side, perfect for crash, since the kids would run towards a surface which is usually solid.
If Hungarian shares the German logic (reinrennen) befutnak could mean crashing into. Even possible that it is meant here? So basically for crash i assume it might really be the same in all three languages, but English would like to run onto when going inside.
But I am not sure what Hungarian wants to say. Especially when the English translation seems to be challenging for native ears. Crash or board?