I don't remember when I first saw Times Roman on a Mac, but I think it was quite a bit later. I'm fairly sure that the first time I saw it was in an implementation of TeX, where it was imported from the UNIX world. I could be wrong about this, though.
The font known as "Times" on the Macintosh font menu, would use one of the following depending upon whether bold or italic text was selected: Times-Roman; Times-Bold; Times-Italic; Times-BoldItalic. The Helvetica font would use Hevletica, Helvetica-Bold, Hevletica-Oblique, or Helvetica-BoldOblique. The Symbol font would simply use Symbol, regardless of whether bold or italic was selected.