What is the difference between natural theology and transcendental theology?

Question

According to wikipedia,

Natural theology, once also termed physico-theology, is a type of theology and deism that seeks to provide arguments for theological topics (such as the existence of a deity) based on reason and the discoveries of science, the project of arguing for the existence of God on the basis of observed so-called natural facts, and through natural phenomena viewed as divine, or complexities of nature seen as evidence of a divine plan (see predestination) or Will of God, which includes nature itself. This distinguishes it from revealed theology, which is based on scripture and/or religious experiences, also from transcendental theology, which is based on a priori reasoning.

Isn't a priori reasoning included in natural theology (see SEP)? Why are natural and transcendental theology being distinguished from each other then?

Answer 1

From your quote, natural theology includes reason and the discoveries of science, whereas trascendental theology does not need to include such discoveries. See also the SEP entry you link (bold mine):

the project of arguing for the existence of God on the basis of observed natural facts.

Observed natural facts are not needed for rational arguments in trascendental theology; see Kant's original definition:

Transcendental theology aims either at inferring the existence of a Supreme Being from a general experience, without any closer reference to the world to which this experience belongs, and in this case it is called cosmotheology; or it endeavours to cognize the existence of such a being, through mere conceptions, without the aid of experience, and is then termed ontotheology

Answer 2

From SEP:

Kant’s distinction between Deism and Theism is intertwined with his distinction between Transcendental Theology and Natural Theology (A631/B659–A632/B660). The meaning of these terms, however, are not what some have assumed (e.g., Wood 1991).

In his Lectures on the Philosophical Doctrine of Religion, Kant defines “Transcendental Theology” as the “recognition [Kenntniss] of God by means of concepts of pure reason” (AK 28:596 [1821]). These concepts are not, however, the pure concepts of the understanding, but rather what he calls the four “classes of concepts” (B110): namely, quantity, quality, relation and modality. More precisely, Kant sees Transcendental Theology as a consequence of reason’s quest for the unconditioned condition, with its concepts of God corresponding to the unconditioned for each of the “classes of concepts”, namely: ens summum (quality), ens entium (quantity), ens originarium (modality), and ens realissimum (relation).

As Transcendental Theology employs no “information” about the conditioned (i.e., the created world), it is without the resources needed to develop a concept of God “in concreto” (AK 28:1020 [1817]). Absent the “materials for the concept of God from empirical principles and empirical information” (AK 28:1020 [1817]), Transcendental Theology can do no more than attribute to God “what is true of him as a thing in general” (AK 28:1020 [1817]). That is, its concept of God is just that of unconditioned quality, quantity, modality, and relation.

Absent all “information” about the conditioned, Transcendental Theology is thus without the resources to develop the concept of God used in either Natural or Moral Theology, i.e, the “wise author of nature” or the judge and “ruler” of nature, respectively (AK 28:452 [1968], AK 28:596 [1821], AK 28:1002 [1817]). Consequently, Kant claims that Transcendental Theology is inadequate, yielding “only a silhouette of a theology” (AK 28:605, AK 28:452 [1968]). Its conception of God is “useless” (AK 28:596 [1821]), “unusable” (AK 28:452 [1968]), and “quite superfluous to us” (AK 28:1020 [1817]). For it provides us only with the god of Deism, and according to the lectures, this God is “useless” and “unusable”.

Hence, despite the familiar-seeming term, Kant does not mean by “Deism” how it was typically used by the British. Their Deism is rather much more akin to what Kant means by “Theism”, as the outcome of Natural (vs. Transcendental) Theology. That is, Kant maintains in the Critique of Pure Reason that our picture of nature as having systematic unity commits us to seeing nature “as if” it were created by a “Wise Author” (A644/B672–A645/B673).