Mayor Bloomberg’s elder daughter, Emma, and her husband are back in New York, having received joint master’s degrees from Harvard University’s business school and Kennedy school this spring.

In August, Ms. Bloomberg will join the Robin Hood Foundation, and Christopher Frissora will start work at Morgan Stanley. The couple, who wed two years ago, has purchased a two-bedroom condominium in TriBeCa.

A lot has changed in New York since Ms. Bloomberg decamped to sleepy Cambridge, Mass., in 2005, but perhaps most important is the increasing speculation that her father will run as an independent in the 2008 presidential election.

If all the conjecture proves true, Ms. Bloomberg may find herself a rival of another presidential candidate’s daughter who lives in New York City: Chelsea Clinton, whose mother, Senator Clinton, is actively seeking the Democratic candidacy.

“I’ve never met her,” Ms. Bloomberg said when asked if she had solicited Ms. Clinton’s advice on being a first daughter.

The two would probably hit it off. They’re close in age (Ms. Clinton is 27, Ms. Bloomberg is 28), live in New York, and attended prestigious universities. Ms. Clinton is a Stanford University graduate and earned a master’s degree at Oxford University. Ms. Bloomberg earned her undergraduate degree at Princeton University before enrolling at Harvard.

Both have played parts in their parents’ political aspirations, but in dramatically different ways that would likely shape the way they get involved in the race of 2008.

Ms. Bloomberg and her sister, Georgina, 24, a champion equestrienne, spent their teenage years watching their father build Bloomberg LP into a booming information business. His political aspirations surfaced when Emma Bloomberg was a young adult, and she wound up working on her father’s mayoral campaign and then in the bullpen of City Hall for $1 a year. She participated in the Principal for a Day program at P.S. 247 in Bensonhurst, Brooklyn.

All in all, being the daughter of an elected official appears to have been a positive experience. She had the mayor of New York City officiate at her wedding. She also has a dormitory at her undergraduate alma mater named after her, thanks to a gift from her father.

Ms. Clinton has more experience with the political spotlight’s harsher glare. She was born after her father had been governor of Arkansas for two years and spent her teenage years at the White House, after arriving at 12 with curly hair and braces. Her national initiation included having her looks mocked by Rush Limbaugh and in a (subsequently edited) “Wayne’s World” sketch on “Saturday Night Live.” There were also perks, such as meeting heads of state and celebrities. Perhaps Ms. Clinton’s most important moment came when she appeared with her parents after the Monica Lewinsky scandal broke.

More recently, her love life and Manhattan outings have been a relatively chaste staple of the gossip columns. She is currently dating a Goldman Sachs banker, Mark Mezvinsky. Both have said they do not talk to the press.

At the Prospect Park Alliance’s Junior benefit Thursday, Ms. Bloomberg and her husband seemed more at ease. It was easy to imagine them hopping out of a helicopter on the White House lawn. Ms. Bloomberg was even willing to talk to the press about the possibility of a possible presidential run by her father.

“Whatever he decides to do, I’ll support him,” she said in an interview. “But I know he loves being mayor and wants to serve his full term.”

Careerwise, Ms. Bloomberg and Ms. Clinton seem to be headed in different directions. Ms. Clinton is working for a hedge fund, Avenue Capital Group, after a stint at the management consultancy McKinsey & Co. Ms. Bloomberg has entered the nonprofit sector, known for its low salaries. She will be working for the executive director of the Robin Hood Foundation, David Saltzman.

The organization aims to fight poverty through carefully supervised grants to more than 100 nonprofits in New York City that work in the areas of education, job skills, survival, and early childhood and youth development. The foundation raised $71 million at its fund-raiser in May. Ms. Bloomberg was among the 4,000 guests at the event, where Aerosmith performed. “It was amazing,” she said.

Perhaps Ms. Bloomberg will meet Ms. Clinton on the job, as the bulk of the Robin Hood Foundation’s donors are from the hedge fund industry. (The group has recently received scrutiny from Washington for investing money in hedge funds managed by board members.)

If they do meet, a safe subject would be philanthropy, a passion they share with their fathers: Ms. Clinton serves on the board of the School of American Ballet; Ms. Bloomberg is on the board of Prospect Park Alliance. Both have served as fund-raising event chairwomen, with Ms. Bloomberg taking the role just last Thursday for a party with the theme “Havana Nights” that was attended by 400 guests and raised nearly $50,000.