I rarely toss in responses anymore. (Pretty much a ghost on the forum now) but I will say that what are asking is hard to describe.
I don't have extreme disphoria like a lot of my brothers here, but I do dislike my chest. Your question may be better answered with the ladies.
However, I'll take a stab. Keeping in mind I don't have extreme disphoria, I don't like my chest. The best way I can put it in lay terms is that I hate the weight. I was heavy for a while, and it feels similar. I disliked feeling heavy, or fat of you will. Now that I'm just about in shape, my chest retains that sensation. It's out of place, like it shouldn't be there. It's a part of my body as much as my legs, arms or waist, but I dislike it. Imagine having water balloons attached to your body and being unable to get rid of them. At the moment I can't think of a better way to describe it.
As far as a difference, I notice a difference when I bind versus when I don't. When I bind, everything is secure, no bulges and I feel comfortable. I won't say normal, because I personally don't think anyone is 'normal'; the human experience is too vast and complex to say that there is a 'normal'. But I feel comfortable, like that is how my chest should be. I remember when I was young and before the dreaded trainer bra was introduced, however. When my chest was like everyone else's, I felt comfortable. I never cozied up to growing breast, and I never wanted them. It never felt right. It was like someone glued something to my chest and I could not rip it off no matter how hard I tried; and my scars show that I certainly did. As an adult I can appreciate the sensations during sex with my partner, but as a gay man he appreciates the nipple sensation and could care less for anything else about my chest. Personally, once I get surgery my life will be more comfortable and enjoyable.
If I'm not clear, I apologize. It's late where I am and I have to be up early.