Here is an example that helped me understand the difference between "if" and "only if" a little better.

Situation One: Only if

You can enter the Mickey Mouse clubhouse only if you’re 21 or older.

So, if someone is inside the Mickey Mouse clubhouse, they must be 21+.

But just being 21+ doesn’t guarantee you entry into the Mickey Mouse clubhouse. Maybe you didn’t buy a ticket, maybe Mickey Mouse doesn't like you because he saw you flirting with Minnie Mouse.

So, if you're inside the Mickey Mouse clubhouse, you must be over 21. But simply being 21 doesn't guarantee you get into the club; it's merely a requirement.

Necessary...........ONLY IF..........Must be true for it...............

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Situation Two: If

You can enter the Mickey Mouse clubhouse if you’re 21 or older.

Being 21+ is enough to get in. But this rule doesn’t say anything about people who do get in without being 21. Maybe todlars get in too. Maybe Goofy gets a free pass. This rule doesn’t stop that.

Sufficient.............IF.......................Enough to cause it ............