WASHINGTON — A few hours after Donald J. Trump publicly backed away from a $1 trillion tax cut for small businesses, campaign aides on Thursday privately assured a leading small-business group that Mr. Trump in fact remained committed to the proposal — winning the group’s endorsement.

The campaign then told the Tax Foundation, a conservative-leaning Washington think tank it asked to price the plan, that Mr. Trump had indeed decided to eliminate the tax cut.

Call it the trillion-dollar lie: Both assertions cannot be true.

At issue is whether Mr. Trump’s plan would tax small businesses, partnerships and other “passthrough” entities at the same 15 percent rate as large corporations, as he proposed last year, or whether they would continue to pay individual income taxes, at rates as high as 33 percent.

The campaign’s conflicting accounts of its own proposal are particularly remarkable because Mr. Trump and his advisers have taken months to refine the details, which Mr. Trump, the Republican presidential nominee, unveiled in an economic policy speech on Thursday in New York.