I get alot of questions regarding the differences between interfacing, stabilizer, and webbing. It doesn't help that sewists of all skill levels use them interchangably.
Interfacing can be fusible or sew-in, woven or non-woven, very very thin to medium weight to cardboard stiff. It is meant to stabilize (here we start with why it can be confusing) or provide structure for projects like bags or garments pieces like cuffs, collars, and plackets. Interfacing is left in the project, not removed. It is applied to the wrong side of the fabric, with a hot iron if fusible or basted if sew-in. Fusible fleece is also considered an interfacing and is thick and little puffy. You'll typically see bag patterns utilize its unique qualities, like the Bohemian Carpet Bag.
Stabilizer can also come in different forms--check out my post about it here. Unlike interfacing, it is meant to be removed from your project. Its temporary hold provides support for thread heavy work like satin stitching, decorative stitch work, and machine embroidery. Choose wash-away, tear-away, or cut-away depending on your design and final project. I used it for these personalized holiday napkins during MD's recent free mini classes.
Fusible webbing (not to be confused with the strapping) is fusible on both sides. You can use it to apply a piece of fabric onto another piece (why it's super handy for applique) and keep it in place while you more permanently stitch it down. It comes in multiple weights--like super hold, if you are hoping to not stitch afterwards and therefore need a more permanent hold. There are several brand names (Stitch Witchery, Heat n Bold, Trans Web, Steam a Seam, Wonder Under) but all are characterized by an almost spiderweb look that when pressed with a hot, steamy iron turns to glue. It's usually paper-backed to help prevent the glue from getting on your iron while applying one side. Applique is a fantastically creative technique and Anna Joyce is a great teacher to show you the how-to's and inspire your design, like with these stockings.