. . . alibis . . . appetite . . . rather . . . Mark . . . [audio source]
The first two a’s are different in their phonetic symbols in the dictionaries from the other two, but I can’t differentiate. What’s the difference between /ӕ/ and /ɑ/?
I think the problem is to do with the accents represented in the audio source.
The vowel in appetite might be better represented as /a/ rather than /ӕ/. This is the value of the TRAP vowel in many younger RP speakers.
The person who says Mark sounds as if she is a Northern English speaker. Northern English speakers often lack the back /ɑ/ vowel, and they also tend not to lengthen their vowels as much as Southern English or RP speakers. I would say that the vowel there is [aː] rather than [ɑː], and not a very long [aː] at that.
I'm not surprised that you can't hear the difference very clearly. Dictionaries which try to represent British pronunciation use RP (Received Pronunciation). Unfortunately they do not attempt to capture other British accents. Some dictionaries are changing the way they are representing the short vowel, using /a/ instead of /ӕ/. (The Oxford English Dictionary is moving in that direction for British pronunciations.)
So one is a front vowel and the other is a back vowel. They also differ in their degree of openness.