The mean the same, however in England i would normally say motorbike in every day speech, motorcycle seems slightly more formal

I agree with Nina with regard to UK usage. For British English speakers, 'motorbike' is the usual everyday term. 'Motorcycle' is the more formal term. You would see this in official notices, such as police signs about where you are allowed to ride or park. In the UK, it would sound rather odd and old-fashioned to say 'motorcycle' in normal conversation. I believe this would also be the case in Australia, NZ and other countries which use predominantly British English.

US: They mean almost the same, but "motorcycle" is the more common term. Everyone will understand you if you say "motorbike." The very short, slangy term is "bike." So if someone said "I rode my bike into work today," you may want to clarify if they meant their motorcycle or bicycle.

In the United States, they are pretty much the same "motorcycle" is much more common than "motorbike," but "motorbike" is used and understood. For short, motorcyclists may be called "bikers." (And to keep the difference clear, increasingly people who ride bicycles are calling themselves "bicyclists.") "Motorbike" is informal, almost a nickname. Sometimes, "motorbike" is used to suggest a smaller, lighter vehicle, but there isn't any precise distinction. In the 1964 hit, "Little Honda," the Beach Boys sing: "It's not a big motorcycle, just a groovy little motorbike; It's more fun than a barrel of monkeys, that two-wheel bike; We'll ride on out of the town, to any place I know you like." https://youtu.be/qZOGlgVldAs?t=33

I can't speak for the whole country but where I'm at on the east coast of the USA, motorcycle is the more common term.