These documents are similar and are often used interchangeably. While they vary a bit from each other, they are used for the same purpose which is to show intent and an agreement to agree. Most are considered "nonbinding" unless the wording is included to make it binding.
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.