The one that works the way you like is <p id="tagline">
The one that is too close to the logo is <h1 id="tagline">
Since that is really a heading it should be enclosed in heading tags, like the second example. Once you get all your pages #header-wrap the same you can style that h1 so it appears the same every time.
...oops, forgot the most important part.
This is the main difference between the two, your paragraph tagged tagline gets this where your h1 tagline does not -
margin: 15px 0;