The term non-Human referred to species or qualities that were not Human, but not necessarily non-humanoid (including individuals who both did and did not resemble Humans biologically and visually).
John Frederick Paxton divided sentient species into two groups: Human and non-Human. (ENT: "Demons", "Terra Prime")
In 2267, while arguing the Vians' right to live in service to Vaal, if they so chose, Spock criticized Leonard McCoy for "insist[ing] on applying Human standards to non-Human cultures." (TOS: "The Apple")
In 2365, Jean-Luc Picard questioned Dr. Katherine Pulaski as to the nature of his duplicate's brain waves, whether they were non-human or artificial. (TNG: "Time Squared")
During Data's Starfleet career, as of 2368, he had encountered 1,754 non-human races. (TNG: "Darmok")
According to Data, the intron virus would affect non-humans just as it did Humans. (TNG: "Genesis")