The key here is the third definition of Schema, that of Kant; if he's not the guy that re-introduced the old Latin form of the word, then he's certainly the guy who popularized it, and brought it to such common usage in our modern language. Etymology Online and Google Ngrams both place its entry into English at about the same time as Kant's work; Webster's and a few other dictionaries place it about 60 or 70 years later. The difference is probably due to the lack of popularity, or common usage as the term slowly worked its way into standard English.
In any event, Kant's idea of a "schema", when translated to our current understanding, is something like "the fundamental, intuitive ordering principle which people use to establish categories, whether mental, sensory, or 'transcendental'." For instance, the category of "quantity" must be ordered by number; thus, "number" is the "schema" of the mental category we understand as "quantity".
A "scheme", however, is essentially a plan or idea that one implements towards a certain goal; but there are exceptions, as when we say "color scheme". If we all spoke more strictly, this would probably be 'color schema", but in fact, "scheme" and "schema" are very, very close words, both derived from one Ancient Latin/Greek word, and so in casual usage can seem interchangeable to folks like you and me. Since scientists no longer rely on "schema" as an important term of scientific practice, or debate, it has lost the institutional rigor it once enjoyed and is now slowly morphing together with "scheme".
Except for one instance: schema is never a verb, and can only be a noun. So that is where the confusion comes in; "schema" used to be a rigorously debated scientific term, part of the "meta-discussion" that surrounded early science, but that era has, for all intents and purposes, long disappeared. Now lacking any formal body of usage, "schema" mostly just hovers on the edge of our standard vocabulary until somebody needs a clear-cut noun for "abstract principle of ordering", or some such.
But often as not, people are lazy enough to just drop the "a" and use the word as "scheme", so.....