A grant maker is someone who gives money to charity in order to further their own objectives and meet statutory responsibilities. This could be at a national or local government/council level, a public body such as the NHS, or a private body such as the National Lottery.
Statutory grant makers do not make grants because they are sympathetic to a cause - unlike trusts and foundations. Grant makers may fund some core costs and provide funding over a number of years. Most grant makers have stringent criteria, a more involved application, and a more complex decision making process. They normally make their criteria and application forms publicly available and have a specific person dedicated to managing the fund.
The application form for a grant could be anything from a general letter similar to the trust application letter, or a detailed form wanting all of the same information, plus extras such as:
Applications for grants take a lot longer to put together, but there is usually a larger financial reward if the charity is successful. However, make sure you weigh up the staff time spent on applications against the financial rewards, to decide whether it's worth the effort and whether you have the resources to cover it, or whether you could outsource the work.