"The new government of Prime Minister Kevin Rudd says it will apologize for past mistreatment of Australia’s Aboriginal minority when Parliament convenes next month, addressing an issue that has blighted race relations in the country for years."
"As a girl, Mari Melito Russell felt out of place. She was darker than the other kids at school, she felt more comfortable in the forest than her suburban home and she had vivid dreams of an Aboriginal woman beckoning her."
Suppose we had no idea what these two stories, dealing with the same issue, were going to be about. The first lead from the New York Times answers the four questions: 1) who (Kevin Rudd, Prime Minister); 2) when (next month); 3) where (Australia); and 4) what (an apology to Aborigines).
The AP lead takes a different approach. This lead is an anecdote about an Aboriginal girl and her life in suburban city in Australia. It reads like prose; it doesn't answer the four questions right away but instead chooses to open like a story and then relay the hard facts further down the page.
So why would these two writers choose to start their stories in such different ways? It's a matter of style. One author thought it best to write a traditional story whereas the other decided to take a more colorful approach. Obviously not every lead has the same format. If every lead were the same, the publication would become difficult to read. Imagine if every lead were like the AP example--the reader would have to sift through vignette after vignette to get to the meat of the story. Conversely, if every lead were straight facts like the New York Times example, the reader might find the newspaper to be dull and drab.
These aren't the only two ways to write a lead. There are countless more. But whatever way the author chooses to write the lead, the goal is always the same: to engage the author in the material right from the start and to get him or her to read the second paragraph.