As in your sex is the physical trait & gender is the mental.
Most of the time they fall right in line with each other but just as with everything in humanity there is a variance (like straight men who act very effeminate or Butch women, would you say that they were ill? or just "different?")
But isn't this just another way of saying the same thing? To be transgender means to self-identify as the opposite sex. Is that correct?
Is it true that an effeminite man identifies himself as a woman? I thought that was an unrelated issue. I wouldn't lump these things together. There is actually a thread here on femininity and at least one poster commented that she felt forced by society to behave in a feminine way. But I don't think that meant she considered herself male.
As to difference vs illness, I am hesitant to say anything because of the potential direction of this conversation. I try to respect the way people live their own lives and I'm not here to approve or disapprove of others. Nor am I out to "cure" the transgenders of the world, if that's even possible. Are you happy with the way you are? If you are then I'm not going to say you should change.
But if you really want to know, I think most people suffer from one form of mental illness or another, of varying degrees. It could be anxiety, depression, or a phobia. My amateur and unqualified opinion is that many people suffer because they are unable to accept some aspect of reality, which creates internal conflict. Sometimes the cause is conscious, sometimes it's not. And both environment and chemistry can contribute. I think that rejecting ones sex is a pretty serious form of illness, rather than just a different path of development (like a girl being a tomboy), but whether it's something that can be changed, or if it's worth changing? That would depend on the individual circumstance.
Anyway I know that someone will interpret this to mean I'm a raving bigot, despite all the qualifiers, but that's what I think.