A bit of a 'What-If' situation has cropped up in our group. Nothing that has caused any table drama, mainly something that has been noticed by some, and debated at the table off-line and casually, but may in fact stand a feasible chance of coming up during session, so some other eyes on the situation could be helpful to avoid a potential halt at the table.

The scenario is as follows:

Wizard casts Invisibility at 3rd rank to encompass himself and one other party member (We'll say the Fighter).

We all know if Fighter attacks, he's no longer Invisible, that's fairly straightforward.

The point of debate, however, is if the Wizard casts a non-concentration spell, ending his invisibility, would they or would they not lose concentration on the spell and also subsequently cause it to end on the Fighter at the same time?

One side of the table contests that it would not end for the Fighter because while the effect of the invisibility ends for the Wizard, it does not make sense that the spell overall would immediately cease to provide the benefit if there was no logical reason why Concentration would be broken, and the first line of the spell,

"A creature you touch becomes invisible until the spell ends."

Means that they simply lose Invisibility, and nothing else, meaning if it really worked out, the Wizard would be Concentrating on a spell that is currently providing no actual benefit, but the spell isn't technically over.

On the flip side, the other side argues that the text of the spell, specifically the last sentence,

"The spell ends for a target that attacks or casts a spell."

Would mean that the moment the Wizard casted a spell, the Invisibility as a spell, regardless of how many Creatures were affected, quite literally ends and Concentration is broken, revealing the Fighter, as the Wizard was a target of the spell and the text states that spell would end if they casted.

In short, the debate seems to be the definition of what exactly "The Spell Ends" means in this scenario; that merely the spell's mechanical effect ends, or that the literal spell-slot consuming ability ends as if Concentration was broken.

The additional end condition affects creatures separately

This is what

The spell ends for a target that attacks or casts a spell.

means. If this addendum was not there, it would mean that the spell, as a whole, ends. This limits the effect. Also, you can concentrate on spells that do not target or affect you, this case is no different.

The spell continues for the other targets

When you cast the spell at a higher level, you basically create multiple instances of the spell for each target. All of these instances are governed by your wizard's concentration.

As you have already noted(Emphasis mine):

The spell ends for a target that attacks or casts a spell.

This indicates that the spell instance for a specific target is terminated when the specified target attacks or casts a spell, the other targets remain untouched by this effect.

Concentration

The casting of a spell that does not require concentration, does not break the concentration of the caster (see PHB p.203), so the wizard is able to maintain the effect on the fighter for the duration or until either the concentration is broken or the fighter attacks.

Therefore, as long as the wizard maintains concentration, other targets can remain invisible if only his own instance of the spell is broken.

Multiple instances

Additionally, to better understand the concept of multiple spell instances, imagine the same setting where the wizard targets only other creatures for his spell.

At the time of casting, he creates the spell for the other creatures. He will need to concentrate on the spell instances to keep the spell going.

For the wizard, however, there is no spell active on him at all. That does not mean that there is no active spell. He is still able to maintain the instances on the other targets.

So, getting back to your original situation, when the spell ends for the wizard, the spell is no longer active for him. Due to the description that the spell only ends for a single target, it makes sense that the wizard can maintain spell even when the spell is no longer active for him.

Only the Wizard would become visible; the Fighter would remain Invisible

In context, the meaning of the phrase "the spell ends for a target" means that the spell effects no longer apply to that creature, and that if they were the last target affected by the spell, then the spell would properly end.

Spells like Invisibility often are phrased using a singular target even when they might have multiple targets. One example is with the spell Mass Suggestion, which has multiple targets yet still uses singular pronouns and grammar when describing its effects on a specific target:

Each target must make a Wisdom saving throw. On a failed save, it pursues the course of action you described to the best of its ability. The suggested course of action can continue for the entire duration. If the suggested activity can be completed in a shorter time, the spell ends when the subject finishes what it was asked to do.

[...]

If you or any of your companions damage a creature affected by this spell, the spell ends for that creature.

This sets a precedent that the phrasing of a spell "ending" is often used as colloquial shorthand for "this spell no longer affects this creature", not that the spell as a whole has literally stopped in its entirety. If the spell were intended to end for all creatures affected because one of them was no longer affected, the spell's description would say so explicitly.