aquariuscsm, the first YouTube video clip you linked is -- without question, IMHO -- the distinct rattle of a VTC actuator that has failed. That sound, like piston-slap, is very frustrating to listen to (and is more pronounced in cold weather, typically), but neither will result in a damaging mechanical failure. In other words, the sound you can hear in the clip is the result of the VTC actuator failing or having failed. (The actuator is slow to retract.) Again, frustrating, but relatively benign.
Piston-slap, in contrast to sound of a VTC actuator, typically continues for several minutes, diminishing in volume as the pistons gain heat and finally reach operating temperature. The two sounds, in other words, are very different and distinct. Fortunately, piston-slap is also somewhat benign. Over the course of time -- often years and thousands of miles -- piston-slap will scuff the cylinders on either side of the piston (opposite the direction of the wrist pins) and result in greater oil consumption. Still, because this issue usually is only present in k-series motors with 80k-100k miles, correcting the problem (i.e., honing the cylinders & replacing worn pistons) is vastly more expensive than periodically adding motor oil.
Footnote of sorts: Increasing the oil weight from a 0W-20 or 5W-20 weight oil to a 5W-30 isn't going to negatively affect the actuation of the VTC actuator. The difference in viscosity (15% or so) just isn't that significant with regard the operation of the actuator. Now, if you want to get into a discussion of what might have prevented or delayed the onset of piston-slap in a k-series motor, that's something worth debating.