They're the same: you and the railway have agreed what you will do (normally, give them some money) and what they will do (not take you to court) in return. So if you have settled out of court, but someone is asking you 'Have you ever been taken to court?' you can honestly answer 'no'. But if they are asking 'Have you ever been taken to court or come to an out of court disposal?' you will have to answer 'yes'.
(Edited in the light of
@AlterEgo 's better informed post above)
These are different from each other. If you are interviewed under caution, that means that you have been warned ('cautioned') that what you say is being recorded and you may be asked to explain what you said in court: So whoever is interviewing you thinks you may have done something wrong and could use what you say to prove it. This sort of caution doesn't mean you have done anything wrong: the police (or whoever) may have made a mistake.
A Police Caution is different. It means that the police have decided that you are guilty (and probably that you have admitted it) but rather than take you to court they are giving you a warning ('a caution').
So if the railway or the police talked to you and said something like 'I must caution you that anything you say may be written down and used in evidence in court'* and you are now being asked 'Have you ever received a caution?' then you can answer 'no'.
" Yes, I know there are precise words. But I can't remember them.
