The English language is unregulated, unlike French and Spanish, for example, which have academies who decide these things and (try to) impose them on an often unwilling population.

Hence, there is no-one to say what abbreviations are are 'correct', except where the prescriptors have full control over the texts as in the example given in Jeux de Mot's answer, or there is some overriding governing body whose prescriptions are imposed by law.

When authoring stuff for my own publications, I never abbreviate million or billion, except when referring to scientific units (where I follow the ISO rules, which have force of law in some areas of human endeavour, e.g. 'M' for mega = million, as distinct from 'm' for milli = thousandths), and in financial texts where my in-house style guide is atuned voluntarily to that of the Telegraph, with the space mentioned by Jack.

Summarising: there is no one-size-fits-all 'correct' solution.