Interfacing and stabilizer have some similarities but are not the same thing.
Interfacing (both sew-in and fusible) are meant to reinforce and stabilize areas of a garment, typically, although they are used to stabilize and reinforce other things. They usually have a little bit of give, even the non-woven ones, so they would not be suitable for something like machine embroidery.
Stabilizer on the other hand is a non-woven material that does not give at all. It is used to...well...stabilize fabrics so they don't distort and pucker when doing machine embroidery, for instance. There are many different kinds of stabilizer- cut away, tear away, wash away, self-adhesive, etc. You could also use stabilizer to stabilize the background fabric when doing applique. It also tends to be more expensive than interfacing.
Some people will use tissue paper, freezer paper, or newspaper or other kinds of papers as stabilizers that are removed after the project is constructed (paper piecing is a good example).