Presidential Reconstruction is usually used to refer to the plan advanced by President Andrew Johnson after the death of Abraham Lincoln. Essentially, Johnson pursued a highly lenient approach to Reconstruction. He offered a pardon to almost all former Confederates who would swear allegiance to the Union, allowing them to return to positions of political power in their states, which could be readmitted upon accepting the Thirteenth Amendment. Most significantly, he showed no interest in using the powers of the federal government to promote equality, or even the well-being of the millions of formerly enslaved people in the former Confederacy. He allowed whites in the South to enact their own laws for dealing with freedmen, which gave rise to the harsh "black codes" that emerged in 1866.
Congressional Reconstruction was initiated in 1866, by Republicans who sought to wrest control of Reconstruction from the President. They passed the Civil Rights Act of 1866 over Johnson's veto, a measure intended to promote black equality. They also passed the Fourteenth Amendment, which gave the rights of citizenship to freedmen, and reestablished the Freedmen's Bureau. Beginning in 1867, they passed a series of Reconstruction Acts that forced Southern states to come up with new constitutions, allow for black suffrage, and other measures before being readmitted to the Union. Sometimes called "radical" Reconstruction, this represented an unprecedented effort to use the powers of the federal government to enforce equal treatment of African Americans.
These are contrasts between the two plans for Reconstruction, but the comparisons are limited. Perhaps the best points of comparison are what these plans did not do. They did not enact any meaningful land reform in order to provide for African Americans. Nor did they expand the franchise to women, a point many woman suffrage advocates made clear with the passage of the Fifteenth Amendment.