The difference is only one thing, you can list any type of element next to .mainHeader for example, #mainHeader a p code div nav span ul li. This will give all of these elements with an ID of mainHeader the CSS you place in the { } for that element.
I'll give you an example.
HTML:
<div class="mainHeader">This text is black because "mainHeader".</div>
<a class="mainHeader" href="#">This text is black because "mainHeader".</a>
<p class="mainHeader">This text is black because "mainHeader".</p>
<nav class="mainHeader">This text is black because "mainHeader".</nav>
<span class="mainHeader">This text is black because "mainHeader".</span>
CSS:
.mainHeader div a p nav span {
color: #000;
}
Update(1): Please understand that doing this is recommended if you are going to give multiple elements the same aspect for a specific thing. An example of this usage, say you want div a p to have the same color, you would achieve this by div a p { color: #000; /* color your wanted */ }