Someone needing their space means they need time for themselves for a while due to: not feeling well, bad day at work, long day with the kids, etc. Basically, a timeout to regroup. Not wanting to be around someone is extremely different. The relationship is over, done, finite. Let's move on in Life without each other.
Sometimes they can be one & the same. If you have no current issues with your partner & they want time out it could be they need to relax & chill out by oneself. But if there's been lots of unresolved conflict this time could be to decide if it's over & time to say goodbye.