Vice President Kamala Harris has made an expanded child tax credit central to her campaign, and former President Donald J. Trump boasts, “I doubled the child tax credit.” With a quick look, voters might think the child-rearing subsidy the rare matter on which the rival candidates agree.

It is anything but. The common vocabulary masks profound differences over which parents the government should help and what constitutes fairness for children in a country of great wealth and inequality.

Mr. Trump sees the $110 billion program mostly as a tax cut, which as president he increased to $2,000 per child and extended to high-income families. But his policy denies the full benefit to the poorest quarter of children because their parents earn too little and owe no income tax.

Ms. Harris would expand the tax cuts and add a large anti-poverty plan, sending checks to millions of parents with low pay or no jobs. That would turn a tax cut into an income guarantee, in a landmark expansion of the safety net.

Supporters of the Harris plan say the payments would shrink child poverty. Critics see an expensive welfare scheme that could weaken the willingness to work.

“They’re both talking about something called the ‘child tax credit,’ but they’re not at all talking about the same policy,” said Scott Winship of the conservative American Enterprise Institute.

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