As I read it, the font did exist and was used in set type, but in was never a typewriter font in the form that it is seen in the documents. It was apparently part of the original Mac fonts in 1980, then adopted by MS as well.
Times Roman, and Times New Roman might be exactly the same font, different names merely reflecting the licensor of the font; Monotype or Linotype.
Newsgroups: comp.fonts
Subject: Re: What's the difference between Times Roman and Times New Roman?
From: Charles Bigelow
Date: 5 May 1994"Times Roman" is the name used by Linotype, and the name they registered as a trademark for the design in the U.S. "Times New Roman" was and still is the name used by The Monotype Corporation. The face was developed by The Times newspaper for its own use, under the design direction of Stanley Morison. Originally cut by the Monotype Corp. in England, the design was also licensed to Linotype, because The Times used Linotype equipment for much of its actual production. The story of "The Times New Roman" can be found in Stanley Morison's A Tally of Types, published by Cambridge University Press, with additional, though not quite the same, versions in Nicolas Barker's biography of Stanley Morison, and in James Moran's biography of SM. (There should be an apostrophe in that name, "Times' Roman", I suppose, though no-one uses it.)
During WWII, the American Linotype company, in a generous spirit of Allied camaraderie, applied for registration of the trademark name "Times Roman" as its own, not Monotype's or The Times', and received the registration in 1945.
In the 1980's, all this was revisited when some entrepreneurs, desirous of gaining the rights to use the name, applied to Rupert Murdoch, who owned The Times; separately, a legal action was also initiated to clarify the right of Monotype to use the name in the U.S., despite Linotype's registration.
The outcome of all of the legal maneuverings is that Linotype and its licensees like Adobe and Apple continue to use the name "Times Roman", while Monotype and its licensees like Microsoft use the name "Times New Roman".
During the decades of transatlantic "sharing" of the Times designs, and the transfer of the faces from metal to photo to digital, various differences developed between the versions marketed by Linotype and Monotype. Especially these became evident when Adobe released the PostScript version, for various reasons having to do with how Adobe produced the original PostScript implementations of Times. The width metrics were different, as well as various proportions and details.
Full Article: http://www.truetype.demon.co.uk/articles/times.htm