Radius definitions I work to:
A radius is an arc bounded by it's max and min limits and located either by tangency points with adjacent surfaces, or by a specified origin point on the drawing. It can't have flats or reversals, and usually has finish requirements.
A full radius has adjacent tangency points that make it 90 degrees of arc.
A true radius, as already stated, is called out when a drawing view has a foreshortened radius depicted.
Hope this is useful.