Font and font family. How to understand where what is?

I understand that the font family (aka typeface) contains fonts. But how it all works in practice is unclear to me. For example, there is a font family Times. It contains some fonts. We also have Times New Roman. What's it? Font or font family? It would be logical to say that this is a font that is contained in the font family Times. But if you look at the definition of what a font is, then...

...the font defines the properties of a particular family member fonts, such as bold or italic, while the typeface defines the consistent style of the font family.Source:

...now it's more like Times New Roman is a font family. If, for example, you look at the same Google Fonts, you can see that there are many different fonts, options for how Times New Roman is displayed.

Or are these all variants of Times New Roman font styles?