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.