Where did "sorry" get its vowel sound?

Solution 1:

The words you list all contain what is called an "intervocalic /r/". As danorton mentioned in his answer, in Received Pronunciation an "o" preceding an intervocalic "r" is pronounced as /ɒ/ (like the "o" in "lot" or "orange"). This pronunciation also occurs in Boston, USA. In Canada, the "o" is pronounced /ɔ/ (as in "cord"). In much of the mid-Atlantic (e.g., New York, Philadelphia, and the Carolinas), the "o" is pronounced /ɑ/ (as in "card"). In the remainder of the US, the pronunciation varies between /ɔ/ and /ɑ/ depending on the word. The words you gave as examples are usually pronounced with /ɑ/, whereas words like "horrible", "origin", and "Florida" are usually pronounced with /ɔ/.

In conclusion, this phenomenon varies by dialect. It is also related to the "horse–hoarse merger," in which the vowels /ɔ/ and /o/ are merged when preceding an /r/, thus making words like horse/hoarse, for/four, war/wore, or/oar, morning/mourning, &c., homophones.

Solution 2:

These two pronunciations are very typical differences in dialect and I suspect that your reference is from an American English dictionary. The first pronunciation is typical of dialects around the U.S. Great Lakes (historically influenced by Irish immigrants — including some of my ancestors) and the second is closer to Standard British (Received Pronunciation).