If you said “if it is a horse it has hooves” you can infer “all horses have hooves” but not that “all hooves creatures are horses”.
Otoh if you said “iff a polygon has 3 sides, it is a triangle” you can infer that all polygons has 3 sides it is a triangle and that there are no other ways to make triangles.
iff is the shorthand for “if and only if”.
If you said “if it is a horse it has hooves” you can infer “all horses have hooves” but not that “all hooves creatures are horses”.
Otoh if you said “iff a polygon has 3 sides, it is a triangle” you can infer that all polygons has 3 sides it is a triangle and that there are no other ways to make triangles.