What’s the difference between interfacing, lining, interlining and underlining?

I am presently working on a fabric constructed hat and there seemed to be a little confusion on the "stuff" used in between the outer shell and the inner shell. On this project it is called Interfacing.
I hope this helps.

Building structure and support into a hat or garment can be confusing and a recent query brought this to light. The question — What’s the difference between interfacing, lining, interlining and underlining?

The answer: All of these terms refer to construction details that are usually hidden from view when you’re wearing a garment, but they serve an important function in maintaining the shape and comfort of your creation.

Interfacing is a support fabric used in areas that need more stability than just the fabric weight. For example, you’ll find interfacing in collars, cuffs, waistbands, closures (like buttonholes), and sometimes hems, as well as fabric hat brims and sometimes hat crowns. In tailored garments, you may find interfacing under entire garment sections, and more than one type used within a single garment.

Lining is used to help hide the inner construction details of a garment, and also to help it slide off and on over other clothing with ease. Lining fabrics are usually slippery and silky, though other types may be used for effect. Lining is constructed separately from the garment and attached at facing or hem areas by hand or machine.

Interlining is a fabric added to a garment when more warmth is needed, like in a winter coat. It may be a heavy fabric with batting added, or a lighter weight one like flannel or fleece. Interlining can be constructed separately from the actual garment (it’s sometimes removable), or used as an underlining.

Underlining is a fabric added to fashion fabric for more body and/or opacity. It’s a separate layer attached to the corresponding garment fabric section wrong side, and then treated as one during construction. The hat underlining fabric is often "fused" to the back of the hat fabric.  Pattern markings are often transferred to the underlining to avoid show-through on the garment fabric.

Sometimes, when we do not want to add additional fabric to summer hats we use 
BIAS TAPE is well known to quilters for finishing the edges of quilts, but bias tape is also a staple in garment and hat making as well. Bias tape can either be store-bought or made at home and comes it in a wide variety of solid colors and prints. You can custom make bias tape in nearly any thickness or fiber content. It’s been said that bias tape is the duct tape of the sewing world – you can use it for nearly everything.

Here we added a bias tape to finished a Dorfman Pacific summer bucket hat.

available at your local sewing center