<ul> is 'unordered list'.
<li> is 'list item'.
And fwiw, <ol> is 'ordered list' and will give you numbers instead of bullets.
The <li> tag is a component of list tags (such as ul, ol etc), so yes - it should be within the <ul> </ul>. You can easily style lists with css though, if you want to lose the indent.
http://www.htmlhelp.com/reference/html40/lists/li.html