Can the frightened condition stack if it’s caused by the same source?

Say Faendal the Fallen Aasimar Paladin uses his Necrotic Shroud racial ability (Charisma saving throw, an affected creature can repeat the saving throw on subsequent turns to end the effect), and a target fails the saving throw and is frightened. On his next turn, while the target is still frightened, Faendal uses Wrathful Smite, which also causes the frightened condition, on the same target and they fail the saving throw (Wisdom saving throw, an affected creature can make a Wisdom check to end the effect).

Does this mean that the target must succed on both the Charisma saving throw and the Wisdom check to end the effect on their turn? Meaning that should one of them fail, the target is still frightened?