No, they are not the same thing. Wave links allow you to bring in one feature solid body (ie solid, point, curve, etc) into your file, without having the tree that created that feature come with it. As long as your link is "live" and not broken, the Wave Link will update automatically with any changes that are made to the original file.
Wave is very helpful for modeling in the context of your assembly - but be careful - it is easy to overuse and create circular references. You can also Link features at a particular timestamp, or break the link purposefully.
Copy Feature will essentially do just that - create a copy of the feature, without retaining any link to the original feature. Any change you make to one, you will have to make to the next.