How can we distinguish between late and lately?

late - 遲到 , 過去的
for example : I am late because the bus was delayed.

lately - 最近
i have been the chief executive officer lately.

lately means recently

LATE：1) 遲到； 2) 時候的遲 (e.g. late at night, late in the morning)； 3) 已故的人 (e.g. the late President Gerold Ford)；
LATELY： 近來

Late and lately are both adverbs, but late is used with similar meanings to the adjective late, whereas lately can only mean 'recently '.
eg. We arrived two hours late. 我們遲到了兩小時。
I haven' t heard from him lately. 我最近沒接到他的來信。
Lately is usually used with a perfect tense of the verb.