Is there a clear distinction between font and font family, for example can we consider Arial to be a font family, but Arial Regular to be a font?
You could consider Arial a synonym for Arial regular, since it's what people usually mean when talking about Arial, or you could consider Arial regular a subset of the larger Arial family that also includes Arial bold, Arial narrow etc. The modern terminology is not clear-cut, but in traditional terms Arial and Arial regular are not fonts:
In traditional typography, a font is a particular size, weight and style of a typeface. Each font was a matched set of metal type, one piece (called a "sort") for each glyph, and a typeface comprised a range of fonts that shared an overall design.
In modern usage, with the advent of digital typography, "font" is frequently synonymous with "typeface", although the two terms do not necessarily mean the same thing.