The LOI as it is now used is a misunderstood application of poorly informed brokers and traders. A more proper application based on established custom and practice in International trade, going back even to the old medieval "Law Merchant" (Lex Mercantilis) is: Buyer requests a quotation _ in modern usage this is an RFQ/Request For Quotation _ NOT an LOI. Seller may then reply with a Quote. Buyer confirms receipt of quoted prices, and requests an Offer.
There are various types of letters of intents for instance if you are applying for university or college then you would need to create a letter of intent for graduate school or university. If you are planning to apply for a job then you would need a letter of intent for a particular job position.