Well, other than the preoccupation with eating, I should have specified. And yes, there really is a connection between them that has nothing to do with fruit or ice cream!
A close-up might help:
See the barely-there stitches where the different fabrics meet? These pieces were made using the "turned edge" applique method, a hand sewing technique where the cloth is folded under itself and the needle is inserted right at that folded edge. This creates a way cleaner border than the regular satin-stitching applique that's done by machine, making it more modern, I think, and more professional looking as well. ('Classy' is the word I want to use, but I think I resort to it just a little too often.) I topstitched the edges afterwards as well since I liked the contrast, but it's not necessary.
Turned edge is actually a pretty straightforward technique, and if you've ever done hemming or whipstitching by hand you'll probably recognize the "moves". I've added a few photos below to explain how it's done when using a simple shape like a square.
|This beige gingham just will not run out.|
You start with the shape you're going to applique (mine was a 1" square with a 3/8" seam allowance), the cloth you want for the background, and a thread that matches the background colour. Remember to single thread the needle, so that your stitches are less likely to show. Then you can press in the edges with your fingertips and nails, and fold in the corners as shown above. Folding the edges in isn't quite standard, but with a straight-edged shape like a square it works really well.
|A single stitch cycle. Out, around, in, and then out again.|
Picture 1: Place the folded square in place and pick a "starting corner." Push the needle up from the wrong side to the right side, making sure that it barely skims the folded edge. See how close the needle is to the fold? It should only "catch" two or three threads on the edge side -- with a firm woven cloth that's more than enough to keep the applique strong.
Picture 2: Pull the needle entirely out and toward your sewing arm. This is mostly a matter of form so that the thread isn't in your way. (Keeping my way clear is also why I stitch counterclockwise)
Picture 3: Insert the needle into the background cloth almost right beside where it came out, but just off the edge of the applique fold. Don't pull through yet.
Picture 4: A few millimeters forward push the needle back up to the surface, this time through the applique cloth. Again, remember to keep it near the edge.
That's one stitch cycle! Keep doing this as you go around the shape. And as a side note, when you do corners it's a good idea to have maybe three stitches bunched there, pretty close together. It'll keep the corner flat and not too pointy.
And you're done! Or I am, at least. Hopefully you will be too, soon, since even simple shapes like this can make for a really nice pattern on a tote or a hoodie, if you make several in a pattern. Good luck!