Vincent Brümmer distinguishes four types of modalities:
1) Conceptual impossibility-impossible by virtue of definition.
2) Logical impossibility-if an assertion that something has been done results in a contradiction, regardless of how one defines the terms used in the assertion.
3) Factual impossibility-things are impossible according to the known structure of reality.
4) Normative possibility-a form of possibility that involves rights and duties (i.e., employees and employers each have prescriptive responsibilities toward one another by means of some formalized agreement).
Some things clearly appear to be factually, conceptually or logically impossible like square circles or events that have happened, then unhappened (Nicomachean Ethics 6.2). Nothing is also red and green all over: that too is factually impossible. Nor is Lebron James both taller than 6 feet and not taller than 6 feet at the same time and in the same respect (law of non-contradiction).
Furthermore, God does not do things that by their very nature are impossible; if one maintains otherwise, he/she land himself/herself in numerous contradictions.
I define logical possibility as "terminological congruity" or internal coherence. The wording is mine, but the idea has been expressed by other writers (Anselm of Canterbury)--something is logically possible when it does not result in a contradictory state of affairs. For instance, there is no logical impossibility contained within the proposition: "All unmarried men are bachelors." The statement is analytically true by virtue of the terms involved. Conversely, to say that "A circle is round and a circle is square" lands one in a terminologically discordant situation: a round and square circle is not logically possible. Yet logical possibility should not be confused with truth or untruth; nor should it be confounded with causal or physical possibility. See Paul Herrick, Introduction to Logic, 61.
Atheists will sometimes insist that the existence of God is logically impossible; however, if this claim were true, then it would mean that predicating God's existence is self-contradictory. Wherein does the supposed contradiction lie? What is terminologically incongruent about asserting, "There is a being such that no being is greater than that being"? The onus probandi falls upon the atheist to explain and demonstrate how the foregoing proposition is logically impossible. But the fact that Anselm's ontological argument is not prima facie incoherent, suggests that atheists who want to deem God's existence logically impossible are guilty of overreaching their target.