A fertility consultant/specialist is a gynaecologist who has specialied in this area. If you need to see a fertility consultant on NHS then you'd need to be referred by GP, just as you would a standard gynae.
A gynae is basically the "standard" name given to someone who specialises in investigation/treatment of the female reproductive organs & functions.....and then they can specialise again to go into fertility, endometriosis etc etc etc (all the different areas of female reproduction etc).
Our consultant is a gynaecologist/consultant but specialises in fertility and is also an obstetrician so he deals right the way through from any initial issues to the delivery of a baby.......and he's NHS and private !
I've also seen another gynae consultant who specialises in fertility but also has special interest in endometriosis.
That does yes. I think that probably applies to my gynea too. I want to go to someone who knows about male IF too though because nobody knows anything and GP won't refer DH to a specialist so I figure if I can get refered to someone who knows I can kill too birds with one stone so to speak.