SANTA CLARA, Calif. — The last time Hillary Rodham Clinton ran for president, she seemed torn over whether to emphasize her chance to make history, or to play down her gender and reassure voters that she was tough enough for the job.

This time there is no question: Mrs. Clinton’s potential to break what she has called “the highest and hardest glass ceiling” is already central to her fledgling 2016 presidential campaign.

But rather than the assertive feminism associated with her years as first lady, Mrs. Clinton’s campaign message will be subtler. It will involve frequent references to being a mother and grandmother and to how her family has inspired her to embrace policies that she believes would help middle-class families.

As one Democrat close to her put it, voters have learned that she is tough; now she can also present herself as a sensitive candidate capable of nurturing the nation at a difficult time.