The strong forms of the words can and that both have the TRAP vowel in RP. This is the same vowel as in the word cat /kæt/. These forms of the words are shown in examples (1) and (3) repsectively. The auxiliary verb can is usually only strong when stressed or when stranded (ie when not followed by another verb).
The subordinator that and the auxiliary verb can both have weak forms which we use when they are not stressed. These are usually said with a schwa vowel, /ə/ as shown in examples (2) and (4). However, can may also be realised with a syllabic consonant, as in /kn̩/.
The determiner that as in that elephant, and the pronoun that as in give me that have no weak forms. Neither does the noun can, of course.
Speakers who are just starting out on their journey into English pronunciation may well mistake a schwa for another vowel. It can be difficult to recognise for the uninitiated, having no association with any particular orthographic vowel.
[Speakers with razor sharp ears may be able to detect a slight difference in the quality of the vowels in can and that. The vowel in can will be nasalised because of the following alveolar nasal sound, /n/.]