I believe what Wiki is trying to say (albeit not very clearly) is that at one time in the UK a wet lease included fuel (which makes sense if you think about the term literally), and a "damp lease" was a wet lease without fuel. In the past, "damp lease" also referred to a wet lease without cabin crew, who would be supplied by the lessee.
However, these days the term "damp lease" is not used very often, and "wet lease" can refer to arrangements either with or without cabin crew.
Common sense is not so common. -Voltaire