Grotesque, but then the strip is called Bizarro.
The pun turns on word division: wi-fi /waj faj/ vs. wife eye /wayf aj/; compare I scream vs. ice cream. (There are also prosodic differences, which, however, are variable along several dimensions.) At a phonemic level, then, the two words are segmentally identical, making a perfect pun.
But along with the differences in word division go phonetic differences: the phonetic realizations of /aj/ in an open syllable (as in wi) are somewhat different from the realizations in a closed syllable (as in wife), for example. Some of these differences are widely shared, but others are associated with regional or social dialects. In particular, for some speakers the nucleus of /aj/ is higher before a voiceless consonant in its syllable than it is otherwise (in an open syllable, or before a voiced consonant), and this difference is large enough to count as a difference in “accent”.
The raising of /aj/ (to [ɐɪ] or on to [ʌɪ]) before voiceless consonants is often treated as a case of so-called Canadian Raising and lumped together with the raising of /aw/ in this context, but /aj/-raising (though it’s common throughout Canada and the northern border of the U.S.) is much more widespread geographically than /aw/-raising (for some discussion, see here, with a later note on /aw/-raising here).
A further refinement: when scholars of variation distinguish one dialect from another (in part) on the basis of a phonetic difference, they’re inclined to say that one dialect has variant X where another has variant Y. But this is a kind of shorthand: in fact, speakers of each of the dialects have a range of phonetic realizations for X and Y, with variation between speakers and according to occasion. X and Y count as different for some set of speakers if the means for X and Y are significantly different phonetically on relevant dimensions.
I mention this because it’s tempting to try to get at dialect differences by just pronouncing some words (like wi and wife), out of context, and reflecting on the pronunciations: “I have [aɪ] in wi, but [ɐɪ] in wife“. That’s quick and easy, and net discussions of variation often proceed on that basis, but it’s not the same thing as looking at the phonetic facts.
That’s the sociolinguist’s standard warning — relevant in this case because self-reports on the pronunciation of /aj/ are often unreliable, for a number of reasons.