Some dictionaries give two variants of pronunciation (with /ɑ/ vs. /ɔ/) for words like: fog, log, loss, etc. I think that the variant with /ɑ/ has nothing to do with the cot–caught merger because those dictionaries give only one variant for words like law (with /ɔ/).
Is there any perceived difference (dialect, style, etc.) between such variants (e.g. /fɑg/ vs. /fɔg/ for fog)?