Late (as an adverb or noun-like expression) — indicating that something is behind schedule or happens after the expected time.
遅くなってすみません。電車が遅れました。
Sorry I'm late. The train was delayed.
会議が遅くまで続いて、帰りが遅くなった。
The meeting went on until late, so I got home late.
遅く来ると席がなくなるかもしれないよ。
If you arrive late, there might not be any seats left.
Slowly — indicating that an action or movement is performed at a slow speed.
彼は足を痛めているので、遅く歩いている。
He injured his leg, so he is walking slowly.
仕事は焦らず、遅くでも確実に進めてください。
Don't rush the work; even if it's slow, proceed reliably.