Does concentrating on a different spell end a concentration spell’s effect?

Question

Some smite spells for paladins have additional on-going effects for a mob hit by them. i.e wrathful smite causes a mob to be frightened until they succeed a wisdom save or until the spell ends. The spell duration is 1 minute and requires concentration.

If a paladins hits a creature with wrathful smite and it fails the initial wis save and becomes frightened, and if the paladin then casts a different spell that requires concentration (like shield of faith) does this change what he is concentrating on, meaning the effects of wrathful smite ends straight away and the creature is no longer frightened as the spell has ended, or does the creature continue being frightened until the minute is over or until they pass a wis save?

Answer 1

The frightened effect ends when the spell ends, and the spell ends when you cast another concentration spell.

Wrathful smite states that the target is

frightened of you until the spell ends.

So when the spell ends, they stop being frightened, and if you stop concentrating, the spell ends immediately. Tasha’s Cauldron contains a helpful list of rules summaries, one of which explains succinctly the rules for concentration:

As soon as you start casting a spell or using a special ability that requires concentration, your concentration on another effect ends instantly

So casting a different spell that requires concentration will end the effects of wrathful smite immediately, and the target will no longer be frightened. The full rules, found in the PHB, reads:

The following factors can break concentration:

• Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can't concentrate on two spells at once.

• [other stuff that ends concentration]