BOSTON — Jill Stein, presumptive nominee of the Green Party, is probably the only candidate on the campaign trail who spends an hour a day cooking her own organic meals — and who was, not too long ago, the lead singer of a folksy rock band.

But the differences do not end there. When Ms. Stein is introduced on the trail as “Jill Stein for president,” she is also very likely the only candidate to be asked, “For president of what?”

That’s what Keith Brockenberry, a cook, wanted to know at a meet-and-greet in Roxbury last week. After one of Ms. Stein’s supporters clarified, “for president of the United States,” Mr. Brockenberry seemed both taken aback and delighted.

“Get out of here!” he blurted out. “I had no idea.”

What Ms. Stein lacks in name recognition, however, she is trying to make up for these days in high-energy organization and low-cost social media outreach. If her application for federal matching funds is approved, she will be the second Green nominee to qualify, after Ralph Nader in 2000 — another milestone for this 11-year-old alternative party and potentially a major boost for a campaign that does not accept corporate donations.