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.
Here's where the difference comes in between a cover letter and a letter of intent. With a cover letter, you likely already have a solid idea of what the job opportunity is, and how to position yourself for it. With a letter of intent, you have to make a slightly trickier balance—positioning yourself as qualified for a job that may not be clear yet. To do that, align your self talk around the company or the industry, making sure to highlight your skills and achievements that would make you a good fit for the company. You can also be specific about your level and experience. For example, you should make it clear that you're looking for a manager-level position if you don't want to be considered for more junior or entry-level roles.