A formal warning is just that a warning about behaviour which may be recorded. A caution is given to an individual who must then accept that they are guilty of the offence and this is also recorded. Neither counts as a conviction. Whether you should inform an employer depend on what they are asking you to say. If you are required to declare convictions, you can stay silent. If you are being asked to declare warnings and cautions, as part of your contract, you must do it or risk the consequences which may be severe .