Yes you are right, the tablespoon on the left is one from an old cutlery set, the one on the right is a measuring spoon.. you are comparing apples to oranges. If you use an VERY OLD English recipe that calls for a tablespoon,used by folks who didn't have scales and before measuring spoons were available in the UK you would be right to use that one, but if you tried to use it in a modern recipe it would be as useless as your other one would be perfect. The recipe you would be using would clearly indicate which you were to use by the way it was written, you can pick out the very old English ones easlily and know you need to use the old serving spoon.
If you compare a UK measuring spoon to a US measuring spoon you would find they are identical. The teaspoons are also identical with the OZ set too.
Bear in mind that the old UK tablespoon that you have was originally used on the table as a serving spoon.
Yes, US cup is 8 fluid ounces. which is 237 mls , UK and OZ are metric and are 250mls, very little difference. I have all three sets of cups and three sets of spoons, simply bcause the OZ set was a gift from my brother in OZ ,came with a book,the UK set I bought before my furniture and baggage arrived from Canada when I was there and I needed a cup and spoon set. I still usually use the orange Tupperware set I bought in the 70s here in Canada.
I taught classes in the UK using baking cups and spoons we used the UK ones but my recipes were from all over the world, mostly American and Australian..
XX Jeannine