Ozzie announced his plans to step down from his role at Microsoft on October 18, 2010
Compared to "resign", "step down" has a connotation of an amicable parting with the possibility of a continuing relationship. The word "resign" is often used when employee parts employer over some disagreement or other negative cause.
If I recall correctly, Bill Gates' active role at Microsoft changed several times without him severing all activity at the company. Saying he resigned might not give an accurate impression unless carefully qualified by the particular role he was relinquishing.
Bill Gates stepped down as chief executive officer of Microsoft in January 2000. He remained as chairman and created the position of chief software architect. In June 2006, Gates announced that he would be transitioning from full-time work at Microsoft to part-time work.
While both step down and resign mean the same thing, step down is used as a phrasal verb to speak of someone resigning from an important position. Ray Ozzie held the position of chief software architect at Microsoft.
To resign is to "quit." To step down is to "climb down" from a high position.
It is possible to "step down all the way," as Ray Ozzie did at Microsoft. In this regard, the two are synonymous.
On the other hand, Bill Gates initially "stepped down" from CEO to Chief Software Officer, thereby taking a lesser post, without actually quitting or "resigning." (He finally fully "resigned" several years later.)
It's also possible to resign as janitor or low level person without "stepping down," because there is no lower level to step down to.