Instead, I find it useful to think about combinations and layers of twos and threes. So the different being talked about in this article is about whether the beat pattern is more of three groups of two, or two groups of three. Convention has mapped those, typically, to 3/4 and 6/8 respectively, but again that's entirely arbitrary.
Likewise 9/8 time is usually three groups of three. 4/4 is two groups of two (though the second two often have slightly less emphasis, whereas 2/4 time is just single groupings of two). 7/8 is a group of three and two groups of two (could be 2-2-3, or 3-2-2, or 2-3-2). 5/4 or 5/8 is a group of two and a group of three.
But ultimately time signatures are just a convenient way to hint at the beat pattern expected, and to give a framework in which to write the musical notation. The actual _music_ is not so easily transcribed.
It's not always easy to pick out what specific signature is being played at every point in the song, but the "suspended" feeling of hanging beats as the signature changes is very obvious.
For example, a 2/2 tempo with 100 BPM is easier to "manage" than a 4/4 tempo with 200 BPM, and they are the same as each 2/2 beat corresponds to two 4/4 beats. So a "Presto" or "Prestissimo" will often be written as 2/2, with half the BPM that it would have in 4/4. Likewise, a 6/4 is usually faster than a 6/8 or 12/8.