p.s.
I just had a look at a hose connector that for some reason was next to the sink.
This is a brass one that must have come with a tap as it is new.
in this case it is composed of a brass screw-on collar, and a nozzle that fits into it. The upstream end of the nozzle fits inside the spout of the tap and seals with a small rubber O-ring. The collar has to be screwed on quite tightly to press it into place.
It's not a common design
I recommend using only the brass connectors and fittings. You can often get a pack of half a dozen different sorts at places like Aldi, in the gardening season. Plastic ones are liable to go cross-threaded and never work again.
I expect your tap has a half-inch BSP thread. Amusingly (?) neither the thread nor the tap nor the hose measure half an inch anywhere you can see. This is because it's a thread thar used to fit on the outside diameter of a thick iron pipe, that had a half-inch internal diameter. Iron pipes are now made a bit thinner, so it doesn't even fit those.
Some big taps are 3/4" or even 1" BSP. These are also not the size their name suggests.
Throughout the world, plumbing fittings are made to fit British Standard Pipe threads.
Your German washing machine has a 1/2" BSP thread on the filling hose, and so does your basin tap and your shower mixer.
There are two other things that, throughout the world, are made with old British threads.