In the US, the act of watching planes (often through binoculars) and likely recording registry numbers, is "planespotting". The same thing, but involving trains, is not called trainspotting, though the public thinks it is. Watching trains and recording locomotive road numbers is "railfanning". "Trainspotting" is not a term/verb here, but it was the name of a movie. The word is well-known here due to said movie, but it does not actually describe anything--but the public thinks it does (they think it means railfanning, since "planespotting" is fairly well known).