The differences between Times Roman and Times New Roman are mostly a trademark issue. Although there are subtle stylistic and spacing differences, they are invisible in body typefaces at normal reading distances.
Microsoft Windows computers feature Monotype's Times New Roman while Mac computers have Linotype's Times Roman.
In digital font systems, Times Roman is usually the first font coded, and the font most often examined to determine the quality of the font system. Therefore, software designers and commercial organizations take particular care with it.