The two methods are designed to do two slightly different things on purpose. Internally they are implemented very differently too. You can take a look at the sources in the documentation and see that .include? is doing a lot more than .cover?
The .cover? method is related to the Comparable module, and checks whether an item would fit between the end points in a sorted list. It will return true even if the item is not in the set implied by the Range.
The .include? method is related to the Enumerable module, and checks whether an item is actually in the complete set implied by the Range. There is some finessing with numerics – Integer ranges are counted as including all the implied Float values (I’m not sure why).
These examples might help:
('a'..'z').cover?('yellow')
# => true
('a'..'z').include?('yellow')
# => false
('yellaa'..'yellzz').include?('yellow')
=> true
Additionally, if you try
('aaaaaa'..'zzzzzz').include?('yellow')
you should notice it takes a much longer time than
('aaaaaa'..'zzzzzz').cover?('yellow')