A Transcendental Thomist is someone who sees themselves as following the thought of Thomas Aquinas and attempts to integrate a kind of Kantian subjectivism into their account. Basically, their epistemology follows Kant in saying that the subject is primarily responsible for experiences, rather than external objects.
Neo-Thomism can mean a few different things, but generally it refers to the revival of Thomism stemming from Leo XIII’s encyclical Aeterni Patris.
Scholasticism and Neo-Scholasticism are too broad for me to take a stab at. I would do some searches and check some encyclopedias. The words are used in many different ways by different people, and are often used in a pejorative sense.
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