Solar Eclipse calculations produce a value called the eclipse magnitude. This is NOT the brightness of the eclipse. The eclipse magnitude is simply a fraction of how much of the Sun's diameter will be covered by the Moon. A magnitude of 0.5 means that the edge of the Moon is at the center of the Sun. The thing is, while magnitude is a simple concept, it requires explanation. As a result a more common term used is obscuration which refers to the area of the solar disk that is covered or obscured by the lunar disk. If 50% of the solar disk is covered, the actual lunar edge is past the center of the Sun.
The obscuration is how much of the solar surface area is covered. It can be calculated directly from the Magnitude using trigonometry. An explanation for the calculation of obscuration given the magnitude is provided at http://www.jgiesen.de/eclipse/
It is important to remember that the angular size of the lunar and solar disks are slightly different. During an annular eclipse, the angular size of the Sun is larger. During a total solar eclipse the angular size of the Sun is smaller than that of the Moon.
As a general rule of thumb, when the eclipse magnitude is 0.6 (60% of the solar diameter covered) then just about half of the solar disk has been covered.
So which term makes more sense to use when describing eclipse circumstances to the general public?
Some prefer to tell how much area has been covered (obscuration) while others prefer the amount of the solar diameter covered (magnitude).
My personal favorite is to explain both if given the time. Yet the question is how to describe the eclipse circumstances for someplace using the fewest terms that will make sense to the reader. "XX% of the solar diameter is covered" uses few words than "XX% of the solar surface area is covered" but requires an understanding of the term diameter. I'd like to think that most readers of such a press release would know what the term diameter means.