As for the non-constructivism definition, is it possible to be a non-constructivist but not a mathematical realist? If not then these aren't really separate definitions.
It may be that all non-constructivists are mathematical realists, but some constructivists are mathematical realists as well (by my definition of "mathematical realism"). So "Platonism == mathematical realism" and "Platonism == non-constructivism" are two different statements. I can imagine a non-constructivist asking "Are you a Platonist?" (thinking "Do you accept the law of excluded middle?"), and a constructivist answering "Yes." (thinking, "yes, valid constructive proofs are valid whether or not any human knows them or believes them.") This miscommunication will lead to confusion later in their conversation.