迟(chí)到(dào)means ‘being late’ and is used when a person is not punctual, for example,
对不起,我迟到了
duìbuqǐ, wǒ chí dào le
Sorry I be late aspect marker
‘Sorry, I am late.’
晚(wǎn) means ‘late’ and it can also means ‘being late’, but can also be used in a broader circumstance. For example,
对不起,我来晚了
duìbuqǐ, wǒ láiwǎn le
Sorry I come late aspect marker
‘Sorry, I am late.’
太晚了, 我们 该 回家 了
tàiwǎnle, women gāi huíjiā le
Too late we should go home aspect marker
‘It is too late, we should go home.’