In the bad example, Jean is too vague, and has a few red flags, like suggesting that her last job didn't end well, and making an inappropriate joke about Scorpios to gloss it over. You can tell people you're great, but it's better to prove it by offering specifics, like she does in the better example. In the second example, Jean's letter body is more clearly organized, and makes sure to give the most relevant details about her career so far.
A Letter of Intent is a written document that outlines a preliminary agreement between two parties regarding the terms of a potential purchase or other transaction. The two parties can settle on certain terms while agreeing to continue to negotiate the other terms and details of the transaction before actually signing a purchase agreement.