Allophones of /ə/
I think you're right about the distinction, whichever IPA symbols are appropriate. In younger London speech, final schwa may be closer to /ɑ/, so 'mother' may be pronounced /ˈmʌðɑ/. But the same speaker would probably say 'potato' as /pəˈtɑɪtɑʊ/ with the traditional schwa in the first syllable.