Much rides on this apparent distinction. Because of it, Mr. Bush and several other contenders have delayed registering their campaigns with the Federal Election Commission, even as they travel the country, meet with voters, attend candidate forums and ask donors for money. That allows them — or so their representatives argue — to personally raise money for and coordinate spending with super PACs.

By law, a campaign and an independent group cannot coordinate their activities. But since there is no campaign, the representatives argue, there is nothing for the groups to illegally coordinate with.

Not everyone agrees. In March, the Campaign Legal Center and Democracy 21, two groups that favor stricter enforcement of campaign regulations, filed complaints with the election commission alleging that Mr. Bush; Gov. Scott Walker of Wisconsin; Rick Santorum, the former senator from Pennsylvania; and Martin O’Malley, the former Maryland governor, all met the legal definition of being a candidate and were raising tens of millions of dollars in violation of federal rules.

Mr. Bush’s comment in Nevada was “a slip of the mask, not a slip of the tongue,” said Paul S. Ryan, a senior counsel at the Campaign Legal Center. “The rules apply to you as soon as you start spending money to determine whether you will run. Simply denying that you’re a candidate doesn’t get you around these campaign finance laws.”

No potential candidate has been more aggressive in using the new model than Mr. Bush. In recent months, his advisers have created a traditional political action committee — the kind that can accept contributions of only a few thousand dollars per donor — along with a super PAC that can take unlimited contributions and is expected to handle the bulk of the advertising on Mr. Bush’s behalf during the primaries. There is also a nonprofit organization, based in Arkansas, that can raise unlimited contributions and is not required to disclose its donors.

All share some variation of the name “Right to Rise,” and Mr. Bush has headlined fund-raisers for the groups, even putting his name on invitations to more than 300 donors who attended a Right to Rise conference in Miami in April.