Similar is a different concept from Difference. Differ is derived from Difference. Differ is a synonym of Disagree. one thing you do when you Disagree is Debate. 
Thin is related to Sheet. Sheet is related to Leaf. Lobby is etymologically related to Leaf. 
Similar <--DistinctFrom--> Difference <--DerivedFrom-- Differ <--Synonym--> Disagree --HasSubevent--> Debate 
Thin <--RelatedTo--> Sheet <--RelatedTo--> Leaf <--EtymologicallyRelatedTo-- Lobby 