Classification of Typed/Untyped Lambda Calculi
Your table is a bit confused; here's a better one.


Untyped lambda calculus -- no logical interpretation, as Andrej notes
Simply typed lambda calculus -- intuitionistic propositional logic
Polymorphic lambda calculus -- pure second-order logic (ie, without first-order quantifiers)
Dependent types -- generalization of first-order logic
Calculus of constructions -- generalization of higher-order logic


Type dependency is more general than first-order quantification, since it turns proofs into objects you can quantify over. Lambda calculi corresponding to ordinary intuitionistic FOL exist, but are not widely used enough to have a special name -- people tend to go straight to dependent types.

You can also relate the syntactic form of a calculus to logical systems, as well.


Combinator calculi (eg, SKI combinators) -- Hilbert-style systems
A-normal form -- sequent calculus 
Ordinary typed lambda calculus -- natural deduction