1) There are different types of skinny. Skinny can mean that you have the body fat percentage of a wire coat hanger, it can mean that you've got a narrow frame, you can be both skinny and somewhat muscular at the same time, or you can be skinny in the sense that your body is defined almost exclusively by your bones. You'll need to figure out which type of skinny you are.
2) What you refer to as the standard skinny guy advice is a way for people who have a hard time gaining weight to manage to gain some mass. Therefore, that advice would be a good idea if, say, you want larger pecs or biceps or quads or the like. That will not be the same sort of advice to follow for your abs, or if, say, you want your biceps to be approximately the same size they are now, but be more defined. In those cases, you want lighter weight at higher repetition levels.
Fundamentally, you've got a couple of different types of fibers in each of your skeletal muscles. The standard skinny guy advice deals primarily with increasing the number of them that are fast twitch--the ones that are used for very short bursts of force, and which are more visible after training. Definition is more based on slow twitch fibers, which are the endurance version--they don't output as much force in the short run, but they also take a lot longer to fatigue. Many (though not all) skinny guys will inherently be better at endurance events, as they've got a higher proportion of the slow twitch fibers, and they're not lugging around as much mass. Many bigger guys will be better suited for sprinting events.
Or, to put it an easier way: if you're skinny in the sense that you have a hard time gaining either fat or muscle, then follow standard toning suggestions (low weight, high rep, cardio), and it'll go much faster for you than for most guys. It's the flip side of it also taking a lot *more* work for you to gain muscle in the first place.