遲 vs. 晚 in Mandarin: when to use which one?
迟(the standard simplified Chinese word, while the Chinese Traditional is 遲) and 晚 both have the meaning of late.


迟 usually means late for the appointed time or a certain time.
example: Party七点开始，你来迟了!—— The party start at 7:00 pm, you came
late! 

The word '迟到' is frequently used to describe late for certain time
晚 is more complex

It has the meaning of late for a certain time.
example: Party七点开始，你来晚了!—— The party start at 7:00 pm, you came
late! 

It also have the meaning of just being late but not for a
certain time. example: 他很晚到家—— He arrived home very late. example:
他昨晚很晚离开—— He left late last night. 

Or it means evening. example:
晚上——evening, example:今晚——tonight, example:昨晚——last night.




Fun fact: to describe public transportation's behind schedule, the word is 晚点, where '点' means the schedule time for public transportation to arrive.