Certain features rely on concentration "breaking" rather than simply ending. To show the difference, there is first the "Concentration" section of the rules which states:
[…] If you lose concentration, such a spell ends […]
Note that this applies to any method of losing your concentration. Then there is the conjure elemental spell, which includes the following:
[…] If your concentration is broken, the elemental doesn't disappear. Instead, you lose control of the elemental, it becomes hostile toward you and your companions, and it might attack […]
Note that Jeremy Crawford has unofficially ruled (tweeted) on this, stating:
Willingly ending your concentration on a spell in D&D isn't the same thing as having your concentration broken. In the rules on concentration (PH, 203), willingly ending your concentration is purposefully not on the list of things that can break your concentration.
He has also tweeted the following:
The distinction between ending your concentration willingly and your concentration being broken is only relevant when a rule tells you it's relevant. The conjure elemental spell is a rare instance of the distinction having meaning, which is detailed in the spell.
The list he refers to is the one under the "Concentration" section, which states:
[…] The following factors can break concentration:
- Casting another spell that requires concentration. […]
- Taking damage. […]
- Being incapacitated or killed […]
Thus, it seems fair to say that concentration can be ended but not broken, say, if a caster decided to stop concentrating on a spell.
The section on "Longer Casting Times" only tells us what happen when concentration breaks:
When you cast a spell with a casting time longer than a single action or reaction, you must spend your action each turn casting the spell, and you must maintain your concentration while you do so. If your concentration is broken, the spell fails, but you don't expend a spell slot.
It does not explain what happens when your concentration ends but hasn't been broken.
So, what happens if you are casting a spell with a longer casting time and choose to stop concentrating? Or perhaps the premise is flawed, and stopping concentration on a spell like this does count as breaking your concentration; if that is the case, I would like to know that as well.
There are only 4 ways concentration can end
They all result in the "end" of concentration, but only the last "breaks" concentration.
With respect to the longer casting time, "you must spend your action each turn casting the spell, and you must maintain your concentration while you do so" - if you don't, you don't cast the spell. In this particular situation the result of "ending" under condition 1 is the same as the result of "breaking".