As a matter of modern terminology it's probably fine to identify "simple type theory" with simply typed lambda calculus, or only say STLC. But in the past it did refer to a somewhat specific flavor of type theory so historians may have hair to split on this topic. Below is a quick summary based on the History of type theory on Wikipedia.
In the 1900s, Bertrand Russell comes up with the first theory of types, or type theory as we call it today. Of course, before a century of evolution, it probably looked quite different from what we're familiar with today.
In the 1930s, Alonzo Church comes up with the untyped lambda calculus. Early on were failed attempts at turning that into a logical system. It was more effective as a model of computation, alongside Turing machines.
In the 1940s, Church comes up with the simply typed lambda calculus, as A Formulation of the Simple Theory of Types.
The purpose of the present paper is to give a formulation of the simple theory of types which incorporates certain features of the calculus of λ-conversion.
 The simple theory of types was suggested as a modification of Russell's ramified theory of types by Leon Chwistek in 1921 and 1922 and by F. P. Ramsey in 1926.
As an additional bit of historical curiosity, apart from the outdated notation, the STLC is quite recognizable in its original formulation:
(2) if x_β is a variable
with subscript β and M_α is a well-formed formula of type α, then (λ x_β M_α) is a well-formed formula having the type αβ;
(3) if F_αβ and A_β are well-formed
formulas of types αβ and β respectively, then (F_αβ A_β)is a well-formed formula having the type α.
And later, type theory and lambda calculus are further intertwined by Curry-Howard, so that nowadays it's acceptable to just confuse the two. But it may still be reasonable to maintain at least some connotative distinction, saying "type theory" to emphasize on aspects that are more logical and "lambda calculus" to emphasize on those that are more computational.