Trump advocates greater accountability for schools and teachers and the ability for families to choose any school, many with government support, while returning more control to states and school districts.
Clinton, allied with teachers' unions, calls for greater pay for teachers, a reduced role for charter schools, universal prekindergarten and rethinking how students, especially minorities, are disciplined.
Both plans call for significant federal investment but in different ways.
Here is a look at how the candidates plan to address primary and secondary education.
Clinton focuses on early childhood and race relations
Clinton has emphasized two elements of the education debate: enhancing programs for children and reforming the way schools, particularly those in black and Hispanic neighborhoods, discipline students.
On the issue of early childhood education, Clinton has proposed universal prekindergarten for 4-year-olds. Her campaign noted about 25 percent of the nation's 4-year-olds are enrolled in a taxpayer-funded pre-K program. The remainder are either enrolled in preschool, daycare or are cared for in the home by family or hired nannies.
Clinton points to data that show children who attend pre-K perform better in elementary school. According to the Center for Public Education, children who attend pre-K are almost 40 percent more likely to be prepared to begin kindergarten as a 5-year-old. They are 35 percent more likely to remain on grade level by age 14 and are 17 percent more likely to graduate high school.
Additionally, universal pre-K would alleviate some of the childcare costs and responsibilities for working parents, while ensuring a safe environment for young children, she said.
Clinton also advocates expanding the federal Head Start and Early Head Start programs for children from poor families. Head Start offers young children nutritional and education support they might not receive otherwise.
On the topic of primary and secondary education, Clinton has advocated for higher teacher salaries in order to address what she termed a shortage of qualified teachers, particularly in urban districts.
Clinton has also called for a decreased reliance on standardized testing, saying districts and the federal government should require fewer tests, but make the ones that are still administered better at gauging students' progress as they get older.
Clinton has not mentioned the controversial national education standards known as Common Core -- an Obama administration-backed set of standards that require testing -- often on the campaign trail. Several long policy papers on her website do not include a reference to Common Core. She was asked about it in 2015 and said she viewed the criticism of it as "painful," though several of the tenants of Common Core are not included in her own education plans.
The Obama administration's "Race to the Top" initiative required states that wanted to receive additional federal funding to adopt a series of policy positions, including more stringent teacher evaluations. The federal government has not, however, mandated states implement Common Core, a program developed by education experts and state governors, which sets benchmarks for education goals at various grade levels, but leaves curriculum decisions about how to achieve those goals to states and individual school districts.
Clinton supports national standardized tests as a means of tracking student achievement but, in keeping with the teachers' unions that have endorsed her candidacy, does not support using those test results as part of an individual teacher's job evaluation or as a factor in determining their pay.
But perhaps the issue that most defines Clinton's education reform agenda is her call to end what she views as a "school-to-prison pipeline" in many inner cities.
Clinton has been highly critical of the "criminalization" of schools' disciplinary responsibilities, as well as suspension rates that disproportionately affect students of color.
Her campaign website points out black or Hispanic students are far more likely to receive suspensions or expulsions than white students who act out in middle or high schools, which results in missed time in the classroom. A recent study by the Graduate School of Education at the University of Pennsylvania found that in the 13 states where black student expulsions are the highest, black teens make up about 25 percent of the student population, but account for more than half of all expulsions.
Clinton has proposed a $2 billion investment in education spending for districts with high suspension and arrest rates to hire support staff to change the culture in schools that rely on zero-tolerance disciplinary policies.
Clinton's funding would be made available for districts to hire School Climate Support Teams, a group of educators and support staff that would work in individual schools with teachers to improve disciplinary practices in the classroom to prevent more serious disciplinary problems from arising. They would also work at the district level, to develop new disciplinary policies that emphasize keeping students in the classroom over suspension or arrest.
The plan would also allow districts that rely on school resource officers to handle discipline to hire additional counselors and professionals with an education background to take over those duties, rather than police officers who are often not trained in the specifics of juvenile discipline.
On charter schools, Clinton has expressed skepticism that they often are not subjected to the same scrutiny and criticism as public schools. While she does not want to eliminate charter schools, she said their role should be limited to their "core mission" as incubators for new, innovative educational practices that can then be replicated in public schools across the country.
Clinton is endorsed by the nation's two largest teachers' unions: The American Federation of Teachers and the National Educators Association.
Trump seeking a return to local control of education
If there is one overarching theme to Trump's education proposals, it is that he prizes local control over crucial decisions to requirements by the federal government.
Trump has criticized federal Common Core standards as "education through Washington, D.C.," a common criticism of the standards by Republicans. Trump has gone as far as to call Common Core a "total disaster."
While Trump has said he wants to improve public schools and the quality of education, he has also proposed a massive federal investment that would allow children from poor families to pay tuition at private or charter schools if they do not want to send their children to their local public school.
Earlier this month, Trump unveiled his education plan, the central element of which is committing $20 billion in federal spending to give to states as block grants that would be passed to low-income parents to enable them to send an estimated 11 million children to a different school if they wish.
While Trump did not say where the funds would come from in the federal budget, he promised it would not be new spending.
He also said converting education funding into block grants would not require states to create what is widely referred to as a school voucher program, though he pledged to campaign for states to do so if he becomes president.
He has also called for the vast downsizing of the U.S. Education Department, which he said puts an undue burden on states and local districts by mandating education policies.
Trump has called for the elimination of federal standardized tests under Common Core. He has not called for the blanket elimination of standardized tests, however.
Instead, Trump has said student test scores should be used as part of a teacher evaluation system that enables districts to reward successful teachers with merit pay, while calling on the end to practices in many states that make it difficult or impossible for some underperforming teachers to be fired.