well it is up to you. if these branches fruit well I would only remove any that cross/rub with others and any that spoil the 'shape ' of the tree.
if you do remove the thinner shoots remember they will develop the fruiting spurs for next year. prune when it is still dormant or the axillary buds will be stimulated to grow compounding the problem.

Hi Elson. Firstly, I am no expert. Just recently I discovered that some apples fruit on the tips of their stems! So if I have those, they are caput! But in the second puc you are holding what looks to me like a ‘water Shoot’ these are very straight and long young shoots and do not produce fruit. You can remove them. The general idea when pruning your apples is a) keep a good open shape so air can flow and sun can reach any fruit. B) keep your tree at a manageable size so you can reach your harvest, and c) increase your yield by removing unproductive growth. The last oneis the tricky part. Look for a good plump bud...no more than half a dozen buds from where your twig meets the branch, and cut just above that bud. This will encorage fruiting spurs. By the way...its a bit late now. Apple pruning should be finished by the time the tree starts growing....December to end of Feb.I would say, in most parts of the UK. As to whether the branches are heading downwards.....I don’t think that matters. Its the ones that head straight upwards that are usually the water shoots. Depends what shape you want your tree to be. But look for the fat buds..they carry the fruit.

Thank you both for the good replies. I think that water shoots go straight upwards Cottagekaren, as you say at the end of your reply, so I think I will leave the shoots in my second photo on the tree. I have also done some things I regret. I knocked off quite a lot of fruit buds when I was moving about on a ladder within the tree - I did not appreciate that the buds become apples. I have also cut back some of the shoots too close to the fruit buds, instead of leaving a quarter of an inch above them. I do not know how much this matters - I could cut down to the next outward-facing bud, but I know it is getting late for pruning now; in fact Spring starts today. Advice on this is of course welcome.
I have been pruning two apples trees since around 2011, and I still find it very vexing. I do not want to cut off a branch or shoot that I should not, because the mistake cannot be remedied. When two branches or shoots are touching each other, I often have a dilemma over which one to remove.
I think that I am under the impression that there is a 'perfect' way to prune, when there probably is not. I have learnt more over the last month, and I feel that I understand more now - which is a good thing! I have just found another really good article called 'How to Prune an Old Apple Tree' on www.finegardening.com which I recommend, though it is from North America.

Yeah...me too. Been growing them for about 10 years now and still not sure what I'm doing. Like you I've read a few different sources. But I think Stera is right...this is something we learn from experience and observation..the hard way! :) Not to worry....even fruit trees are very forgiving..eventually.

I did not realise that there were others as bad as me Cottagekaren - lol.

Elson..welcome, you are among friends! 😀