Cross stitch has a pattern laid out on a grid on a separate paper, unless you freehand the design yourself, instead of having the pattern already printed on the fabric. I haven't actually done embroidery yet but I would say it's only similarities to cross-stitching are when you do the details on cross-stitch, or the finishing touches. You use a lot of backstitch, stem stitch, french knots etc to do the tiny details/outlines on the pictures. These detail stitches are what gives the pictures dimensions and makes circles look more circle-y, instead of some retarded 8-bit nightmare you've tried to create in minecraft or something XD
You can make just about anything you like. I'm about halfway done with my second halloween picture that has a huge moon in it so you can see what the circles can look like when I post it. I will try my hand at embroidery soon though, make some pillow cases that caught my eye a while ago, but reading around it seemed like embroidery is closer to needlepoint than cross-stitching.