What is a Stage?
A Stage is a collection of rounds within a Cup.
Stages can either be a complete group stage, e.g. one round within a Cup or a collection of rounds in a knockout cup.
A complicated example would be:
Stage 1 - 3 knockout rounds 1, 2, 3 advancing to group stages
Stage 2 - the group stage (round 4)
Stage 3 - the final 4 knockout (rounds - 5, 6, 7, 8).
What is a Round?
A round is a section of a Cup stage where teams will play each other to compete.
A group stage can be a round in which entrants compete for a position in the standings.
In a round of a knockout cup teams will play each other once or twice and the winners / losers will advance in the Cup in different paths.
In a semi final round for example the winners usually advance to the final.
What is a Tie?
A tie is the part of a round where entrants (teams) compete.
In a quarter final round for example there should be four ties.
In each of those ties 2 teams will compete in a single or multiple matches to identify a winner and loser.
A tie in a group stage round is a single group stage,
e.g. Group A where 4 teams compete in 6 or 12 matches.