As an American, I’m used to sports having a particular structure for their championship. There’s a regular season, followed by the playoffs, then a championship game / series, then the off season, then it all starts again next year. European soccer seems to have all sorts of different tournaments and championships, some of which seem to be ongoing simultaneously. Let’s take England for example. There’s the English Premier League. But some of those teams also are participating in something called the Champions League. Then on ESPN I see that today Tottenham and Chelsea are playing in something called the English Carabao Cup. There’s also the Europa League, the FA Cup, the UEFA European Championship, and who knows what else I’m missing. Why are there so many different cups and tournaments? How does one keep them all straight. Are some more prestigious than others, or is it more of a “my team won Cup X (or whatever) this year, so that’s the one I care about this year, and if they win Cup Y next year instead, then I’ll care more about Cup Y?”
Considering England: The Premier League has no playoffs, they award the championship to the best regular season team.
The FA Cup is a single-elimination tournament involving teams from every level of English football, from the Premier League all the way down to semi-pro teams. It happens during the regular season, with games scheduled in between league games. The Carabao Cup, more traditionally known as the League Cup, is basically the same thing, but earlier in the season and traditionally considered less prestigious.
Traditionally winning the FA Cup was considered an honor comparable to winning the League title, but the financial incentives for winning it are now negligible compared to the League or European play, so it is becoming less of a big deal. The importance a fanbase attaches to winning Cups is generally inversely proportionate to their teams’ chances of ever winning anything else.
The Champions League is a tournament for Europe’s top teams; the top four teams in the Premier League qualify for it. Note that when you finish in the top 4, that means you get to play in the Champions League the NEXT year, so the roster you go into that with won’t be the same roster that you qualified with.
The Europa League is for clubs that aren’t quite good enough to qualify for the Champions League, and the brand new Europa Conference League is yet a third tier. The winner of the EL and ECL automatically qualify for the next higher level in the following season. Also, at some points teams which are eliminated from the CL and EL can drop into the next lower level rather than being done with European play entirely.
I’ve skipped over some fine details but that’s basically how it works.
To be fair, the USA is one country, whereas Europe is made of of many countries. 
However you are right that there are a lot of football competitions!
OK, this explains the England view.
They have a long-standing all-play-all League (1888), currently divided into 4 divisions. The top Division is the Premiership (the next one down is the Championship.)
The longest running knock-out Cup competition is the FA Cup (1871 )
In 1960, the knock-out League Cup was introduced. It’s currently sponsored by Carabao (so named after them.)
The top finishers in the Premiership qualify for the Champions League (along with loads of other European countries.)
Confusingly, the first part of this competition sees teams in all-play-all pools. The leading qualifiers from the pools then play knock-out matches to find a winner.
There are two other levels of the Champions League, respectively the Europa League and (lowest) the Europa Conference League.
The main reason for all these competitions is money, since there is a huge TV audience (around 350 million for the Champions League final .)
I support Tottenham in the Premier League.
I would like them to win in order:
- Champions League
- Premiership
- FA Cup
- Europa League
- League Cup
- Europa Conference League
Pretty much all countries which have soccer have a similar setup of league+cup+international play. In the USA, MLS does add an American-style postseason playoff tournament, but it also has the US Cup (which started in the thirties IIRC, long before MLS itself) and the North American Champions League is a thing which exists.
England is unusual in that it does two Cup tournaments per year instead of one.
Scotland also has a League Cup as well as an FA Cup. I don’t know about other European nations.
Allow me to pick a couple of nits: The (Lamar Hunt) US Open Cup started in 1913, and - like the FA Cup - includes participants from all levels of the US soccer pyramid. The CONCACAF Champions League (CCL) is for leagues from federations in the North & Central America and the Caribbean.
The three Canada-based MLS teams (and Canadian teams at other levels) have their own cup competition, the Canadian Championship. Mexico’s Liga MX teams have their own Copa MX.
To make matters more confusing, MLS and Liga MX decided to create a Leagues Cup competition between their teams who did not make the CCL - sort of like the North American Europa league. Note that this does not include the Central American or Caribbean nations. This is a midweek competition (played during the season, when regular league games are played on weekends). In 2023, the format will change to take place during a month-long pause in the season with all MLS & Liga MX teams in the mix.
Yeah, this has always seemed weird to me. I’m not a soccer fan, but the sports talk radio station I listen to carries the Atlanta Uniteds’ games, so the talking heads discuss them every so often. When I hear that the Uniteds have to take a day or two off in the middle of their season, to go down and play some Ecuadoran or Mexican team that’s not in the MLS, I’m like, huh? Just seems odd to me. Although I suppose conceptually, it’s really not that different than, say, a college football team playing an out-of-conference school. Except they typically don’t do that in the middle of conference play.
I think Scotland was the first to bring in a league cup, just after WW2. It was partly a continuation of wartime cup competitions, but it was also because the top tier in the league went to 16 teams, with only 30 games and therefore reduced gate receipts. To guarantee some extra games, they brought in the league cup with all teams divided into groups of 4, playing each other home and away before going into the knock out sections.
In the early 60s, England borrowed the idea of the league cup but I don’t think it ever had a group stage.
France had an equivalent to the League Cup, Coupe de la Ligue (I wonder what that means) until just a couple of years ago.
Also, it should be noted that the winner of the Champions League is awarded the European Cup, which long predates the Champions League, and is arguably the most prestigious prize in all of world club soccer. South Americans (whose countries all also have similar league, cup and continental championships) would consider the Copa Libertadores as the top club prize.
ETA: To add more to the mix, the winners of the Champions League, Copa Libertadores, and other continental champions also compete annually for the Club World Cup, although the tournament is not quite as prestigious as the name suggests.
And at some point in the post-COVID future, the Club World Cup is going to expand into a quadrennial 24 team event. This was scheduled for 2021, but now maybe '22 or '23.
Most has been covered, but I want to add that one of the bigger differences for an American audience is that soccer leagues tend to have a promotion/relegation mechanism. That is, the worst teams in a league are demoted to the lower league and the top teams in the lower league are promoted. Depending on how high/low the team is there might be a playoff involved.
How do teams qualify for the FA Cup? How would a semi-pro team from nowhere arrange to get in? How are the draws determined? Randomly?
Basically the clubs in the higher divisions enter the tournament later. The first rounds are knockout matches between teams in the lower divisions. Without looking it up, I seem to recall that clubs as low as the eleventh or twelfth tiers are eligible to participate.
Correcting the post above: the FA Cup only extends to the 10th tier and not universally.
I can’t imagine that there is any money available to pay players in the tenth level of FA.
I was thinking that 10th level would basically be good pub teams. Looking up the English pyramid, there’s a cup for the 9th and 10th tier teams called the Vase. Last year’s winner is owned by Wayne Rooney’s agent and he’s invested 100k in improving their facilities. If he views it as an investment then I would think there’s some pay involved, but I dunno.
The FA Cup is confusing. The top teams don’t enter until the third round, which is really the sixth round because the first three are called “qualifying” rounds. So almost all the tiny teams will have eliminated each other by the time the big boys show up.
All pairings and assignment of home field are done randomly, which is awesome. Last year Tottenham, who were leading the Premier League at the time, had to go to a seventh division club whose pitch was basically just a field behind a bunch of row houses whose tenants could watch from their windows.
Players in the 5th tier in Scotland do get paid - not much perhaps but they are semi-professional. With its much larger population, England will have far more semi-professional teams and I would not be surprised to see them at the 10th tier. Also, I could be wrong about this but I suspect a “good pub team” would still struggle badly against such teams.
League cups and European competitions aren’t the only additional cup competitions a club might be involved in. There are local cups like the Lancashire Senior Cup or the Glasgow Cup that date from the 19th century. Until the 1950s or 1960s top clubs would have taken these seriously and fielded strong teams in them.
According to Wikipedia, Jay Demerit, a former USMNTer, started out on the ninth tier of English soccer making $40 a week in 2003. It was a generation ago, and things may have changed at the lower tiers in the meantime, but I think that’s semi-pro by anyone’s definition.