Is energy from spacetime the same as “Energy from the Vacuum” ?
No. “Space Energy” or “Energy from Spacetime” is energy derived from the geometry of spacetime. An apple gains kinetic energy from the gravitational part of the geometry of spacetime when it drops from a tree (and so does the earth). If the vacuum is considered to be non-empty as in quantum electrodynamics, there might be a similarity in the result, but the concept of ECE is more fundamental and clear. In the ECE theory, the zero point energy comes from the zero’th eigenvalue of the ECE Lemma with harmonic oscillator eigenfunctions. The reader should be aware that “space energy” is a small part of ECE and is not our primary focus. The AIAS is interested mainly in a full geometrical description of physics.