While not excluding General Manager, my impression is that more often the Swedish word means the person in charge of day-to-day operations, one or two levels below the General Manager or MD. The ref below (a cached page) is a good example.

As for General Manager, my impression again is that this role is more usual in non-commercial organisations, often smaller ones. The word 'Manager' alone suggests that this person does not have the legal and financial responsibilities of a company director.

That apart, UK Eng MD is equivalent to US Eng CEO, and these days and increasing number of British job adverts mention CEO.