"Season" is also confusing because the Brits aren't tied to Nielson so there may be multiple seasons per year. (Duck Dynasty is like that, but very few other US shows don't tie season to a year)
It gets a bit loony when you start talking about anime too. Anime is broadcast in what's called a "cour", which is a 13-week set, and as you'd expect, there are four cours per year. In America, we tend to call these "seasons", which seems normal since the cours are usually referred to by the season (Winter, Fall, etc.). However, when an anime spans two or more cours, that may be considered a full season.
I've been confused on numerous occasions when talking about certain series. For example, to me, season 2 of Sword Art Online is the series known as Sword Art Online II; however, people that watch the series based upon American naming conventions consider season 2 to be episodes 15-25. If you tend to watch anime inline with the Japanese broadcasts, you normally consider a contiguous broadcast (e.g. all 25 episodes of Sword Art Online) to be an entire season.
Reading
this article is confusing to me because Brits use the word "series" the way we use the word "season."
You get pretty used to it if you watch the show as they use the word "series" quite often. They'll say something like "This is the last episode of the series" during the last episode of the "season".