To me, John, hot, log, and frog all have the same vowel sound, but dog does not - it's pronounced more like "dawg." To some people, "aw," "ah" and the short "o" sound are the same. I've seen "phonetically" spelled names like Ariauna or pronunciations written out like ta-tee-AW-nah for Tatiana (where I'd say tah-tee-AH-nah). Looking at Australian BAs, it seems they spell that same sound "ar," which always throws me for a loop because I pronounce the "r"!
When my cousins moved to western Massachusetts from Rhode Island where I live, I noticed a change in how they pronounce that sound despite the short distance. I say CAW-fee, sawce, and dawg, and they say CAH-fee, sahce, and dahg. Maybe it's just me and I never learned to speak correctly. I remember having a book when I was very young that said dog, frog, and log have the same vowel sound, and I was like "No, they don't!"