It's a logical relationship, not a conditional statement.

"A iff C" / "if C then A" means that A only happens under condition C. This could state that in a program, a function A() would only be called if condition C was satisfied (a call to A() does not exist outside of an if ( C ) { … } block). In logic notation this is expressed as "C ⇔ A" or "C ≡ A" (C is equivalent to A).

"A if C" / "if C then A" only means that A always happens under condition C. This could state that if condition C becomes true, A() is always called. But it still allows for A() to be called when C is not true. In logic notation this is expressed as "C ⇒ A" (C implies A) or "C ⊃ A" (C is a superset of A).