"Vera likes orange juice but does not like apple juice."
Translation:Вера любит апельсиновый сок, но не любит яблочный.
I understand your interest in the last sentence. It really took a lot of time to me to find out a good explanation, but I couldn't. Sorry.
I can only say one thing: Russians never say:
Вера любит апельсиновый сок, а не любит яблочный.
In such sentences they always use conjunction но or и with this words order. And in generally the sentence:
Вера любит апельсиновый сок, но не любит яблочный
is very close by meaning to this one:
Вера любит апельсиновый сок и ненавидит яблочный сок - Vera likes orange juice and hates apple juice.
And finally if you want to use the conjunction а you should use different words order: ..., а яблочный не любит.
I found this explanation, to which I've added my own examples.
'Но' means that something has occurred is different from the things we expected to happen. "She likes apple juice but does not like apples."
The ‘A’ conjunction always tells us some new or something different from the things were mentioned before. "She likes apple juice and/but does not like orange juice."
So the main difference between ‘A’ and ‘Ho’ is that ‘A’ is not a contradiction, it simply adds some new information into the conversation, whereas ‘Ho’ is a contradiction to expectations.