Which of these headlines is correct?

Both - one is forward looking one looked at yesterday.

Edit:

The Reuters headline refers to the European and Asian markets while the AP headline refers to the American stock market as shares are up due to good news on unemployment and other indicators.

Here's the opening paragraph form Reuters article:

Shares across the world fell for the second straight day on Thursday, pummelled by signs the world's biggest economies were headed for recession after a month of financial sector turmoil."

In teh AP story, the final paragraph states:

"Dow Jones industrial futures are up 149 at the 8,643 level, well above their levels of earlier trading."

So, as you can see, they are talking about different things so both are correct.

The Shares fall as recession fears take grip (Reuters).