I think you're making a distinction that doesn't exist: lambdas are a (written) language - the have symbols, morphemes, phrasing, syntax, semantics, pretty much all the elements to define a language. Just an incredibly small and concise one.
Lambdas have definitions, but they have no communicative meaning to human beings. They have to be bound to words to provide us with a humane way of using them.
The lambda calculus is great at describing computation formally, but says nothing at all about programmer ergonomics. What we really care about is the abstraction capability of "node" or "word", the implementation is encapsulated.
