The main difference between them can be found in the
java API.
java.lang.Comparable - oneObject.compareTo(otherObject);
vs
java.util.Comparator - comparator.compare(oneObject, otherObject)
Can you see the fundamental difference between them just by looking at these method signatures?
In a nutshell comparable is for the "natural" ordering. It applies directly to the class. The class can only implement comparable once, so you can only have one ordering defined this way, hence the recommendation to use the "natural" ordering.
You can define as many comparators as you like for a class, all giving different orderings.
For instance if you had a class "Item" with attributes id, name and price.
You could define Comparable to sort on id.
You could have comparators if at any point you want to sort by any of the other fields. e.g .price.