Weightlifting is the sport that involves competing on the Snatch and Clean & Jerk. Just like Powerlifting is the sport that involves competing in the Squat, Bench, and Deadlift.
Saying "Olympic" before WL is simply to help people who don't know much about it to identify what it is, as many people say they are doing "weight lifting" which is simply working out in the gym with regular weight training, not the actual sport.
Coloured weights are simply for ease of identifiability, because all the plates from 25 to 10 are all the same diameter, unlike with regular cast iron plates.
Red plates weigh 25kg, Blue 20kg, Yellow 15kg, Green 10kg, White/Black 5kg, Red 2.5kg, Blue 2kg, Yellow 1.5kg, Green 1kg, White/Black 0.5kg.
For Powerlifting, those coloured plates are made of steel so that they are thinner and can fit more plates in the bar (as heavy deadlifts can requires over 400kg, which is a lot of plates).
For Weightlifting, those coloured plates are made of a synthetic rubber material (aka Bumper Plates). They are thicker (which is not a problem as the weights used are not as heavy as in PL), but they have a bounce when dropped on the floor. This is because WL training requires the athletes to be able to quickly release the bar if something goes wrong in a rep, in order to avoid injury - as the lifts are performed really fast and often overhead. As the plates are bumpers, they can hit the ground and not suffer or cause any damage.
The plates being bumpers also make it easier to get the bar from overhead back to the floor, as the lifter can simply drop them, instead of having to lower them in steps back to the floor.
As PL does not include any overhead lifts, this is not much of a concern for them. But while bumper plates are not used in PL competition, there's also nothing wrong with using them for training - specially if training the squat outside of a rack with safeties (then you can just drop the bar on the floor if you fail a rep).
