The if/whether distinction is similar to the that/which distinction in that so few people understand the difference, and use them correctly, that the distinction is now lost. So, we've reached the point where there is no difference in common practice (but there is in theory, and anyone can learn it if they want to). So, your two examples will sound like the exact same sentence to virtually every native English speaker. But... the first one means something like "He asked me to say yes if I smoke and to say no if I do not". It's hard to reword it without using the word "whether" again. :D The second one is how most people speak, but it's incorrect. If someone who knows the difference pretends that it says "whether" where it says "if" then this one makes sense. If you don't do that substitution then it means something bizarre like "If I smoked, then he asked me; the rest of the time he didn't." That's, of course, not what people mean when they say it, and that's not how the listener interprets it. But that's what it means. Here are more examples. These two examples are both understood to mean the same thing. But they don't actually mean the same thing according to language rules. In brackets I explain what they actually mean when taken literally. "At the end of a night of speed-dating, attendees let the organizer know if they met someone they would like to see again." [in this case only those who fulfill the condition speak to the organizer; the organizer knows simply because someone is talking to them what the outcome of the condition is.] "At the end of a night of speed-dating, attendees let the organizers know whether they met someone they would like to see again." [in this case everyone speaks to the organizer; they have to tell the organizer what the outcome of the condition is for them.]

When "whether" is used, I would usually say "whether or not". So "whether" implies a contrast, in my mind. So in your example: He asked me whether I smoked or not. He asked me whether or not I smoked. Some people may not use "whether" this way, but I do. When you use "if", it is OK as in your example. I guess someone could say "if I smoked or not", but to me it is less natural. You could not say "if or not".