Painting knives have the advantage of palette knives of coming in a range of sizes, more angular shapes, and with sharper points. Plus the larger crank in the handle means there's less chance of accidentally rubbing your knuckles into wet paint. If you're unsure whether you're going to enjoy painting with a knife, first buy a cheap, plastic palette knife and experiment a bit with this before upgrading to a wood-and-metal knife. The plastic one will always be handy for mixing paint (and is much easier to clean than a brush).
Different shaped painting knives obviously produce different effects. For example, a short blade produces angular strokes while a long blade makes it easy to put down sweeps of color. A painting knife with a rounded blade means you're unlikely to ever accidentally scrape a hole into a canvas, but a you won't be able to scratch into the paint as effectively for sgraffito effects.
Note that although it's called a "knife", it isn't designed to cut like a sharp knife or craft knife. Rather a painting knife or palette knife is a blunt-edged knife, like a butter knife, unless you specifically select one with a blade that has a sharp point.
