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I think Lagrange points are where geosynchronous orbits are possible without constant corrections.
Geosynchronous means the orbital period is a day and relatively circular. Satellites with these orbits basically look down at the same part of the Earth.
Lagrange points are locations along an orbit where gravitational forces balance out with the centrifugal force of the orbit. This does allow less fuel expenditure to maintain.
For the Earth-Sun or Earth-Moon systems, the Lagrange points do not occur at the altitude of the geosynchronous orbit. The Lagrange points are either significantly further away or at a different orbital phase.