Wir haben über die gute alte Zeit geredet.
{vs}: Das Tagebuch erinnert mich an alte Zeiten. Als ich noch ... war.
Both expressions have virtually the same meaning of "the (good) old days", but one takes the singular form Zeit and the other the plural Zeiten.
I wonder what differentiates them?
I cannot think of significant differences. Zeiten may refer to more than one period, e.g., if you wish to distinguish school and college. All in all, they appear to be different expressions and that's it (besides the obvious absence of "gut" in one case).
Consider "Wir haben über gute, alte Zeiten geredet" / "Wir haben über die gute alte Zeit geredet" and "Das Tagebuch erinnert mich an alte Zeiten." / "Das Tagebuch erinnert mich an die gute alte Zeit".
