dnd 5th – How do spells that require an ability test against the caster's spells work?

Minor Illusion is a good example of this. The text (PHB 260) says:

… the creature can determine that it is unrealistic to successfully perform an Intelligence check against your DC spell save.

If a creature under DM control uses its action to investigate the illusion, the DM rolls the d20, adds the creature Investigation bonus (or simply his intelligence bonus if no modifier n is specified for the Investigation technique), and checks to see if it is greater than or equal to saving the caster spell.

If the check is greater than or equal to saving the spell of the caster, the creature determines that the illusion is false.

However, wizards use intelligence, not wisdom, for their spells.

The backup of the magic spell of the DC is 8 + [Intelligence modifier] + [Proficiency bonus].