What beliefs did harding and coolidge share in what ways did their presidencies differ?

Harding and Coolidge agreed with the Republican views of their day. They wanted to US to stay out of European turmoil and to avoid being sucked into another war.
They did not want to maintain a standing army. They believed in fiscal restraint and wanted to curb inflation. They believed in free enterprise and did not want the government to try to manage the economy or interfere with business except for some restrictions on trusts and monopolies.