If it is UK English you're after.
There are two versions of your birth certificate that you can apply to:
- Certificate of birth (aka short certificate) which merely states name, sex, date and place of birth
- Certified copy of an entry (aka full certificate which also states names of parents(including mother's maiden surname, their adress/es, occupations and places of birth.
These certificates can be used roughly the same way as Swedish 'personbevis, for example when applying for a passport.