In a game the position arises by itself, and it may have any number of solutions or none at all. In composition the position is built by an author around a specific idea, and it has to meet strict requirements.
Which gives the solver a useful rule: in a composition the obvious move is almost always wrong. The author has deliberately built the position so that the natural solution fails.
The practical difference for a player: studies are more useful. They sit close to real endgames, they train you to find resources in bad positions, and they do not hand you the length of the solution. Problems train something else - spotting non-obvious first moves and mating patterns.
For a practical player it makes sense to start with studies and orthodox problems: the other genres are fascinating in themselves but do almost nothing for over-the-board results.
In fairness: composition does not replace tactical puzzles drawn from real games. For cutting out blunders those are more useful. Composition works on something else - imagination and persistence in calculation.
Composition has an infrastructure independent of practical chess:
A good way in is one study a day, without looking at the answer until the evening. After a month the way you look at a position over the board changes.
A problem states the exact number of moves (mate in two), usually in an artificial position with many pieces. A study only asks for a win or a draw, with no move count, in a position that resembles a real endgame. For practical players, studies are the more useful of the two.
A unique solution - a second one counts as a defect; economy, meaning not one superfluous piece; legality, so the position could arise in a real game; and a genuine idea rather than mechanical calculation.
Yes, though indirectly: composition trains imagination, calculation to the end and the ability to see non-obvious moves. For cutting out blunders, ordinary tactical puzzles from real games are more useful. Best to combine the two.
A genre in which Black cooperates in being mated: both sides play towards the same goal. There is also the selfmate, where White forces Black to deliver mate to the white king while Black tries to avoid it.
With studies, as they are closest to practical play. One a day, without looking at the answer until the end of the day. The solver's rule of thumb: the first natural move is almost always refuted, and the answer is often a quiet move with no check and no capture.
No arbiter skills required. The app takes over the part that usually stops people from running tournaments at all: who plays whom in each round and who finishes first.
works for ten players and for fifty
for a small group that wants to play everyone
for those who do not need a bracket at all
The bot is constantly improved based on real tournaments. If you need a feature that isn't there yet, message the developers right inside the bot with the /support command. Many features appeared exactly because organizers asked for them, and useful ideas get added quickly.
Related - organizing a tournament, round-robin events, tournament FAQ.