meaning - Difference between "if only" and "only if"

What is the differences between "if only" and "only if" ?

What is the use of each in the sentences? Are there any specific rules for their uses?

"I could get more work done if only there weren't so much noise."

"We will manufacture these handbags only if we can obtain the right leather."

Answer

Consider the following three sentences:

1. If I had the money, I would get the operation.


2. If only I had the money, I would get the operation.


3. I would get the operation only if I had the money.

The first expresses a simple failed conditional. I don't have the money, but if I did, I would get the operation.

The second expresses a failed conditional with greater emotional content. I don't have the money, but if I did, I would get the operation and it really bothers me.

The third expresses a failed conditional, without the emotional content, but with a greater stress on the monetary constraint.