This is the 10077th most frequent Japanese word.
遅
"遅" means "late" or "slow."
Here, '遅れて' is used to describe a delay in the arrival or schedule of the train.
電車が遅れてしまいました。
The train was delayed.
In this sentence, '遅くなりました' illustrates a person's action causing lateness.
申し訳ありません、私が遅くなりました。
I apologize, I have become late.
Here, '遅い' refers to the slow movement or lag of the clock's hands.