There is no difference, other than that we have to draw the line somewhere.
My personal view is that I am uncomfortable with it being as late as 24 weeks and the UK is a bit of an outlier in allowing abortions this late without a medical reason. But I think it's really important that women are able to access safe and legal abortions, and the number of women aborting healthy pregnancies at 23 weeks is really low, so I wouldn't campaign for the time limit to be shortened. Where I live the time limit is 14 weeks, which seems pretty short to me, so I guess my personal comfort level would be somewhere in between the two.
But I don't make the rules, and as many people have pointed out, it's all fairly arbitrary, but you have to draw the line somewhere. Unless you support a total ban on abortion or are advocating for there to be no restrictions at all and abortion to be available on demand even when the woman is already in labour, you must accept that we need to draw the line somewhere and the only question is where you draw that line.
That doesn't mean that a 23 week foetus is a clump of cells or a parasite and a 24 week foetus is a human being with rights. It just means a deadline is a deadline.
When I was at uni our essay deadlines were always at 12pm on a Friday. What's the difference between an essay I wrote and handed in at 11:59am and the same essay which I wrote and handed in at 12:03pm because my printer ran out of ink? It's the same essay. There is no difference except the fact that I missed the deadline.
So some countries think the appropriate cut off point is 24 weeks and some think it's 16 weeks and some think it's 12 weeks. Some countries such as Canada apparently think it's when the baby passes through the birth canal, and yet they can't find doctors to actually perform abortions at full term, and clearly if the baby has passed through the birth canal and you kill it, it's murder, even though it's exactly the same baby whose life you could have legally ended ten minutes ago. Just like the essay handed in three minutes after the deadline is the same essay you might have handed in a minute before the deadline, only now you fail.
If you think about it, the only countries whose abortion laws are genuinely logical are the ones with a total ban, because wherever you draw the line, the embryo/foetus/baby immediately before the cut off point is no different to the embryo/foetus/baby after the cut off point.
But unless you support a total ban, you have to make a somewhat arbitrary decision as to where that line should be drawn. And I think legal flexibility would be more harmful than legal certainty on this point. As I said in an earlier post, if a woman who is 20 weeks pregnant is dithering, it's kinder to focus her mind on the fact that she only has a couple of weeks left to make a decision and at the very least she needs to get booked in for a termination even if she changes her mind at the last minute than it is to let her think she can terminate at any time and then have her desperately searching for any doctor, anywhere in the country who will agree to end her healthy pregnancy at 38 weeks.