Not such a dumb question.
Here is my understanding of events:
When the "great split" occurred in 1895, the administration of the breakaway northern based rugby football clubs referred to itself as the "Northern Union" (NU) as opposed to the "Rugby Football Union" (RFU).
However, implicit in this title was that the game being administered was "Rugby Football".
The competition that the NU established was referred to as the "Northern Rugby Football League".
At the time of its establishment, the NU were playing "Rugby Football", as it was at that time, and had not intended to be playing a different version of the game.
This is why, IMO, that fans in the north of England still refer to the game colloquially as "Rugby".
There were however some relatively rapid evolutionary changes to NU rugby, such as the abolition of lineouts, and most significantly the adoption of the play the ball, that by the time it was introduced to New Zealand and Australia, there were significant differences from the RFU's code.
The inaugural governing body (1908) in Australia was the "New South Wales Rugby Football League", (NSWRFL), and maintained this name up to 1984 when it became the New South Wales Rugby League (NSWRL).
In the southern hemisphere the NU's version of rugby (Rugby League) had been seen to be different since its inception, so that the southern hemisphere Rugby Leagues (NSWRFL, QRL, NZRL) had by 1921 requested the Northern Union to alter its name to the "English Rugby Football League".
The governing body in the UK is still to this day referred to as the "Rugby Football League" (RFL).
So, you could say that Rugby League is an Australian invention :shock:
I hope that American Rugby is able to develop its own unique culture, yet do so without altering the essential fabric of the game.