hit P in edit mode
Ctrl - R to add a loop cut right next to the region, then select the region of interest and press ‘P’ to separate the selection from the current mesh.You may still need to use ‘F’ to create faces inside if you are wanting to close the meshes so they seem solid.
edit: yes, I think you can disregard the loop cut - checked and the separation with P keeps the other region intact.
If you’re trying to separate the pieces while keeping them all within a single object, the easiest method I’ve found is to duplicate (Shift D-key) them, and then delete the originals (X-key). The duplicate will not be attached to the original mesh, but will still be part of the same object.
You could also separate (P-key) and then join them (CTRL J-key) again.