This I think is a good explanation of the "difference":
"• Law is a generic term that refers to all rules and regulations passed by the parliament and are meant to guide the conduct of people.
• Acts are a type of Laws that pertain to specific situations and circumstances. They are passed by the government to let people know the rules and regulations about specific situations.
http://www.differencebetween.com/difference-between-act-and-...
So an act is a kind of law. The only way I understand your text is maybe that in this instance it was used in the sense of "bill" or "draft". By saying "to guarantee that this Act becomes law" they might mean "to guarantee that the bill is passed".
My guess..
Could you let us know which country this is from? Thanks!
The translation workplace 
peer agreement (net): +3
