Is it correct to say a mtf trans woman is a real woman but not a biological woman ?

Yes I would say that's correct. 

No.

They are delusional nutcases.  

Not exactly.  If the "perfect" sex change existed, and a person assigned male at birth with a working pair of testicles and penis etc was able to be transformed into a person with a wide pelvis, short stature, breasts, hairless skin, uterus, ovaries and a wide elbow angle and so forth, who menstruated and could become pregnant and give birth vaginally, that person would still not be a woman socially speaking.  However, we are real women, and even biologically real.  We are not socially women.

Why does any distinction need to be made at all?

3

Is one ever correct in calling a man a woman? 

No. Even if they had actual, functional breasts they would not be "real" woman.