World soccer is easier to understand if you grasp the concept that these are clubs and not franchises like US pro leagues. Anyone who wants to form a club and abide by FIFA's rules and the rules of their national governing federation (the FA, in England) can start one and if they win enough rise through the divisions to the top domestic league.
They can also enter other leagues, tournaments as they qualify for them. In England, clubs compete for the season long league title in each division. They also compete in an NCAA tournament style knockout competition for all clubs in the FA, called the FA cup, where you can get a fourth division team playing Manchester United at their local park field. There is also a lesser tournament for the teams in the Premier League called the League Cup (though it has a sponsorship title these days).
For the teams that finish at the top in the top leagues in Europe qualify for next season's Club Championship under UEFA, Europe version of CONCACAF, called the EUFA Champions League. Bids in the season long knockout tournament are doled out based on the strength of each nations domestic league. England's Premier League gets three auto bids with a fourth team qualifying for a play-in round.
Beneath the Champions League, is the Europa League, it's like the NIT. Teams that do not qualify for the Champions League can qualify for this season long knockout tournament. the EPL's fifth place team usually will qualify for this tournament.
So, during any given season, a club can compete for as many as three or four "Trophies" and the TV money that goes with playing for and winning these trophies. In the end, it's all about money for the club and the prestige necessary to attract top players from around the world.
In a sense, it is exactly what the NCAA would look like without the sham of student-athletes and amateurism.