Rugby league vs Rugby Union

As a very brief history:

• 1845: the first rules of "rugby football" are written down.
• 1871: The Rugby Football Union (RFU) is formed. This is the same body as today's RFU which governs rugby union in England.
• (1880: as well as the union vs league split, 1880 is when the American versions of the game moved from contested scrummages to an uncontested line of scrimmage, thus leading to American and Canadian football today).
• 1895: The Northern Rugby Football Union (NRFU) splits from the Rugby Football Union. The split is not over the rules of the game per se, but over professionalism with the RFU maintaining an strictly amateur stance and the NRFU allowing payments to players. The NRFU is the same body as today's Rugby Football League which governs professional rugby league in England.
• 1995: (yes, 100 years later) The International Rugby Board, the governing body for international rugby union, removes the amateur restrictions on the game. Both codes are now fully professional.

Source: mostly Rugby football on Wikipedia.

Union existed first

Source: Museum of Australia.

All football codes trace their roots back at least 700 years in England which "attracted large and often riotous crowds of players in England from at least the Middle Ages. Banned by royal decree at least 30 times between 1314 and 1667, the game was hard to control and even harder to suppress."

The growth of urban areas and the spread of the railways in the 19th century led to a move to establish general rules of football. A schism between those who wanted to exclude handling of the ball and those who didn't: the former led to Association Football (soccer) and the latter led to Rugby Union, Rugby League and North American football. Australian Rules football has its roots in Gaelic football.

Rugby emerged sometime between 1820 and 1830 at Rugby School:

According to legend, Webb Ellis picked up the ball and ran with it during a school football match in 1823, thus creating the "rugby" style of play. Although the story has become firmly entrenched in the sport's folklore, it is not supported by substantive evidence, and is discounted by most rugby historians as an origin myth.

The first laws of Rugby (always laws, never rules) were written down in August 1845. The game spread to other public (i.e. private) schools across the UK and, with the spread of the railways both schoolboys and ex-schoolboys travelled and played across the country. Because the private schools were the cradles of the British Empire's administrators, they took the game around the world.

Clubs for both soccer and Rugby were established and subsequently peak bodies for organising national competitions: The Football Association for soccer (which is where the name soccer comes from Association Football) in 1863 and the Rugby Union (which is where the Union part comes from) in 1871.

Both were strictly amateur. Players were not paid to play and could not be compensated for loss of earnings if they were injured.

The schism

The founders and controllers of the Rugby Union were mainly ex-public-schoolboys who were relatively wealthy and lived in the south of England.

The growing leisure of the working class and the ability to travel cheaply by train led to an explosion of popularity of the game generally but particularly in the industrial north. The players and clubs there were not wealthy and a football injury could mean not only loss of wages but loss of their job - industrial relations protections being not of 21st-century standard (except 21st-century USA).

At a general meeting of the Rugby Union in September 1893, it was proposed that ‘players be allowed compensation for bona fide loss of time’.

But an opposing motion was raised ‘that this meeting, believing the above principle is contrary to the true interests of the game and its spirit, declines to sanction the same’. The opposing motion was carried 282 to 136 votes and rugby union stayed resolutely amateur.

A meeting in Huddersfield, West Yorkshire on 29 August that year between 21 clubs formed the Northern Rugby Football Union, or Northern Union.

The name 'Rugby League' was coined in 1901 with the merger of the Lancashire and Yorkshire competitions Northern Union, forming the Northern Rugby Football League.

Rugby League and Rugby Union were initially the same game but more than a century of divergent rules changes have led to different but still quite obviously related codes. The two sports are probably the most similar of all football codes to the extent that it's not uncommon for players to switch and for some to earn the title "dual international" for representing their country in both.