This question is related to Is the Weasley's residence "the Burrow" in the magical or non-magical realm? and explores an apparent inconsistency, given only the Harry Potter movies as source material.
The Hogwarts Express line seems to have an inconsistent existence between magical (invisible to ordinary humans aka muggles) and non-magical (muggle) realms; platform 9-3/4 is clearly hidden from muggles, but in Chamber of Secrets, when Harry and Ron take the car (in the muggle world) to catch up to the train, they make no explicit crossing into a magical realm, suggesting that the train is traveling the muggle world despite its departure from a magical platform.
In which realm (magical or muggle) does the Hogwarts Express exist? How is this apparent inconsistency resolved?