This is the difference that can be described as philosophical belief. The belief that a child is who they say they are when there is no possible way for them to be what they say they are. Words such as ‘understanding’ and ‘recognition’ are used to attempt make this identification meaningful.
Let's unpack this.
Affirmative approaches say that we should recognise a child's neuro-cognitive / psychological experience of sex (gender) for exactly what it is.
That psychological experience is real; it is part of who someone is, just like being autistic or being gay is a part of who someone is.
To recognise that psychological experience is not to promote a false "belief", it is to recognise what is real.
Now what can that recognition and understanding involve?
The first step is really simple. It can involve listening to the child and taking them seriously.
"I hear you when you tell me your a girl. That's what you feel. I hear you when you tell me that matters to you deeply.
I hear you when you say it hurts you so much when I call you a boy.
I'm not just going to say "that's nice dear, you're a boy, now let's go to the park", because I hear your pain and your pain matters to me".
What else can recognition involve?
Can we change their chromosomes? No. A child born with XY chromosomes will always have XY chromosomes, and there's no use pretending otherwise.
But can we change the words we use to address that child - to 'girl' and 'she' instead of 'boy' and 'he'?
Of course we can. That's as simple as speaking one word instead of another. You might say we shouldn't do that because then words will lose all meaning and society will collapse. I disagree of course, but that's a different debate - it's about what we should do, not what we can do, and that involves a meaningful consideration of the various consequences of both approaches, not just declaring "we can't do that! Because it's a lie!"
What else can we do?
Can we change the person's physiology to create functioning female reproductive anatomy? No. That child will never grow up to be a woman who can give birth. We shouldn't pretend otherwise.
But can we give that person Oestrogen therapy and testosterone suppression to alter some of their secondary sex characteristics to reduce some of the psychological distress associated with body dysphoria? Yes we can - we can give them feminising hormones so that they grow breasts, redistribute fat, have reduced muscle mass and body hair growth, for example.
Should we do that? At and what age?
Again - those are questions that require meaningful consideration of the benefits, harms and risks of doing so, versus doing nothing. There's no use simply trying to shut the conversation down by pretending it's impossible.