What is the difference between 'Equals' and iff?

I was musing and realized that it's not too easy to see what the difference is between $A = B$ and $A \iff B$. Can anybody explain the difference, if there is one?

I may be being stupid but I can't see how you would think they were the same.

If you replace an iff with an equals, the statement won't usually make sense.

Can you give an example of why you think they are the same?

"Two plus two equals four" is true, but "two plus two iff four" doesn't really make sense.

Why not? Assume $((0++)++) + ((0++)++)$ is a true statement. Then by the definition of addition. $((((0++)++)++)++)$ is true. But by definition this is 4. And so 4 is true if 2+2. Repeat for the other relations and possible truth-values. What's the problem?

In what way is ((0++)++)+((0++)++) a statement? Correct me if I'm wrong, because I've never studied formal logic, but that doesn't appear to be a statement to me, just an expression. The statement ((0++)++)+((0++)++)=((((0++)++)++)++) is true.

In logic, I don't think there is much of a real difference between equals and iff. I'd always reserve iff for logical statements and equals for arithmetic statements, though.

Yes, that seems to be the convention but I just wasn't sure if it was simply a convention or was based on some subtle difference in their definition. In retrospect, I don't seem to know enough about either maths or logic to say if it is anything more than a convention in maths (or if the convention comes from a logical background). I don't even know what the difference is in logic - my textbook is unclear on it*. So, all in all, probably best to leave it until I know more. ;no;

*It initially defines equality as a predicate but then treats it almost exactly like a connective, and it defines iff as a connective. Unfortunately, as arithmetic in logic is plain nasty, I have no idea what kind of object "4" is.

I'd say there was a slight difference between them - two statements can imply each other without actually being exactly the same statement, even if they're "equivalent". I'd have defined equals as "x = y if, given any statement p, p(x) if p(y)". Hmm, I don't know either. Perhaps better to wait till someone more experienced comes along.

Very roughly, it seems that equals has the possibility of connecting individual 'objects' (but don't ask me to define that!); it does not appear that iff can connect objects meaningfully - it needs to connect objects with properties? (That seems to be what you are saying, and it makes sense with what I know...)

I'll be nice to you = you give me some cake (bad example, but still).

I don't see how anyone could possibly think that. There may be some situations where they could be used similarly, but there are hundreds where they're completely different. F iff ma???? I'll be nice to you = you give me some cake (bad example, but still).