For me, if I were the hostess at a dinner party, I think the use of 'some' would suggest I was rather hoping my guest would say 'yes, please!' I might use 'would you like any chicken?' if I rather suspected my guest wasn't too keen, and might say no. On the other hand, I'd often use them interchangeably. "Would you care for any/some coffee?" sound much the same to me. They are both open-ended: yes, I would like coffee/no thanks/Do you have tea? I might expect any answer, and I wouldn't mind what the answer was.

I read them as the same.

Yes, I think you have it. The meanings overlap. But consider a festive meal with many dishes on the table, and there is clearly far more on offer than anyone can eat -- fish, veggies, pasta, etc. A host who is serving their guest is then likely to say "Would you like any chicken?" because they are anticipating a possible refusal, which would not be at all impolite in the circumstances. However, if someone comes for dinner and the main dish is chicken with 2 veg, then "some chicken" is more likely.