When you save a mesh, the resulting saved mesh reflects either the high-fidelity geometry or the low-fidelity geometry, whichever is currently set according to:
The Display menu commands Use Mesh for Low-Fidelity Geometry and Use Mesh for High-Fidelity Geometry, or equivalently
The corresponding toolbar icons.
To save the mesh, use the File > Save Mesh or File > Save Mesh As command. For details, see Save Mesh Command.