What's the Difference?
Many people get confused about letters of intent and letters of inquiry, but you don't have to worry. Just think of a letter of intent as a form stating that you intend to apply for a grant. In contrast, a letter of inquiry is more like a sales pitch, in which you describe your project in the hopes of being invited to submit a complete grant proposal.
In a letter of intent, you are telling the granting agency that you plan to respond to a request for proposals. These letters are often sent to governments, since they are the agencies that usually issue RFPs.
Sometimes the granting agency doesn't request a letter of intent at all. If they don't ask for it, don't send one. The agencies that do request letters of intent do so simply to learn how many project proposals they can expect to receive. Sometimes, they might also be interested in finding out from which geographical areas potential proposals will be submitted.
When you write a letter of inquiry, think of yourself as a sales representative. Your letter of inquiry describes your project and asks for permission to submit a grant proposal. These letters are usually sent to foundation-type funders. Increasingly, foundations are requiring letters of inquiry as the first step in their grant-proposal cycle.
Use a letter of inquiry when the foundation guidelines request this step and/or when you are unclear about whether the foundation funds the type of project you wish to present.