@crafter both terms are used, sometimes both are used on the same package. Like Kwaaked I have both awls and stilettos. I collect vintage sewing tools, since I was a kid really, and to me there is a difference. Awls tend to taper from the point and the shaft can get rather big. This is useful when you need to force a larger opening as you just keep easing it into the fabric or leather til you get the opening you want. My stilettos, I have a bunch, are pointy but then most of the shaft is the same diameter the rest of the way up and tends to be longer than on an awl. I have different diameters of stiletto. It's useful if you're needing to replicate the size of an opening, like in some heirloom stuff or a bunch of eyelets on one garment. The tapered shaft of an awl can make uniformity harder to do. Stiletto's are also useful to guide fabric under the presser foot. It's handy for me to flip the 1/4" quilting seams the right way.
My favorite awl is a Victorian one made from ivory. Or, more likely bone, but I like thinking of it as ivory.