I can see no clear difference between these two words. They both refer to financial aid that is given by a giver to a receiver. Givers are often government bodies, either local or national, but not always. Receivers can be other government bodies, corporations, small businesses, academic institutions, NGOs, private individuals. The grant/subvention will be defined by the giver and then the word grant or subvention will be specified. Colloquially we talk about getting a grant, eg. to study, but in business it would perhaps more often be referred to as a subvention.