The most common cushion or pillow type must be the "knife edge" cushion. One look at this style and it is easy to see why it has that name. A knife edge cushion can have just a simple seam where the fabric is sewn together, as seen below.
Or a knife edge cushion can have what is called a welt. Also commonly called a cord--or sometimes referred to as "piping"--a welt is a piece of rolled fabric that trims the edge of the pillow. A self welt is one that is made out of the same material as the cushion or pillow.
But look how fun a pillow can be with a contrasting welt. If done with light and dark colors, the effect can be very striking, looking like a bold outline.
A knife edge cushion can be a little plain so to add some elegance to a pillow, try a Turkish corner where the material is pinch pleated into a discreet fold. The overall look is softer and more luxurious.
Another common cushion and pillow style is the box edge. Instead of sewing two pieces of material together to form a seam, a box cushion has side panels that give it a top, a bottom, and four sides, just like a box.
A flanged cushion is one whose edge extends beyond the seam, as seen here. The flange can be of the same or different material.
Sometimes the material used for the flange can be gathered into a kind of ruffled look that lends a feminine or country appearance.
Pillows can also be trimmed or edged with a variety of fringes, tassels, and pom-poms.
A bolster pillow is mostly used for decorative purposes. It is usually seen at the ends of a sofa, or as part of a pillow arrangement on a bed. The example below in silvery velvet is a bolster with a darker welt and a button tufted end.
When you go cushion shopping, keep an eye out for these styles.