I used to be right there with you! Before I learned how to applique, I had no idea what people meant when they said they did the applique by hand! I thought they literally stitche around the edges with a needle and thread.
My appliques are all done "by hand" I find an image I want to use and either print it out or trace it DIRECTLY from my screen. I then trace each piece of the image onto a fusible web (like heat n bond lite). If it's a simple applique like a Mickey head it is only the one piece but id it is a pieced applique like a princess, I cut out each feature- hair, eyes, arm, dress, face etc. It then gets pieced back together like a puzzle. I usually trace my facial features on before I piece and iron it to the bodice. That way I know where to stitch (either with a needle and thread or my machine) later. The I use my machine set to a satin stitch (or a very closely spaced zig-zag) and applique around the pieces. I do the fine detail work - eyelashes, outlines etc. LITERALLY by hand.
Machine appliques are done on an embroidery machine. Some you can purchase premade designs (you see the same images alot) and "upload" them to your machine and the machine does the stitching for you. You still cut the fabric and place it, but the machine does the actual satin stitch. Some of the designs have over a dozen steps to them. You can also buy a program and digitize your own images (Heaher has done this)
I like doing the appliques by hand. You can do any image you find. The machine appliques are usually PERFECT (when done right) but you are limited on your designs (unless you can digitize your own

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Aimee's adorable princesses she just posted were done "by hand" (awesome job, BTW) and the other Jasmine was done by Heather on her embroidery machine.
Did that help clear things up at all?