An oil paint stick is exactly what it sounds like, oil paint in a stick form. It's formulated differently to the oil paint that comes in a tube (they've got some extra wax in them) so it can be shaped into a stick or crayon shape. A thin skin forms over the dried paint stick; this comes off when you apply pressure this comes off and you're then got buttery paint.
You hold an oil paint sticks directly in your hand and draw with them like you would with an oversized pastel. But oil paint sticks are not the same thing as oil pastels. They're softer and squishier, and have less wax in them.
An oil stick doesn't dry (or, rather oxidize) to same extent as oil paint, as it has wax in it which never oxidizes completely. It does dry to touch-dry, but if you had areas of thickly applied oil stick, the wax in the paint means you could mangle it. "The linseed oil [in the oil paint stick] will get fairly hard and the paint will feel dry to the touch, but if someone were to push against [a thick layer] it would yield to pressure and deform."
