There are three somewhat separate questions - what the Rehabilitation of Offenders Act permits employers and others to ask for UK purposes, what is disclosed by various DBS checks, and what foreign governments require from people wishing to enter their country.
Any conviction punished by a fine is “spent” for the RoOA 12 months after the date of the conviction. Most employers and others in the UK are not entitled to ask you to disclose spent convictions. There are, however, exceptions where this restriction does not apply.
Most offences which cannot be punished with imprisonment are not usually ‘recorded’ and are unlikely to appear on any DBS checks. Regulation of Railways Act s 5 (3) (a) has a theoretical possibility of a sentence of imprisonment so this will be recorded and returned on DBS checks.
How these two, and the concept of filtering for DBS checks, interact is more complex than it should be.
Neither of these change the position in relation to other countries. A person who wishes to enter another country must respond accurately and honestly to any enquiries and read the conditions of any application very carefully.