這兩個短語都表示「散發，發出」之意，一般可以換用，但側重點有所不同。
give off通常用來表示「散發，發出」某種氣體或氣味。如：
Boiling water gives off steams.
開水散發出蒸汽。
This milk must be bad, for it is giving off a nasty smell.
牛奶一定變質了，因為它散發出一種令人噁心的氣味。
The chimney no longer gives off volumes of waste gas into the atmosphere, as protective filters are being used.
加裝了防護過濾器以後，這煙囪已不再向空中散發成股的廢氣了。
give out 則通常用來表示「散發」某種光，聲，熱，信號等物理現象。此外，它還可以表示「分發，宣布，耗盡」等現象。如：
The leaves gave out a whirring sound.
樹葉發出沙沙聲。
The sun gives out light and heat to the earth.
太陽向地球發出光和熱。
The ship gave out radio signals for help.
船發出無線電信號求助。
The government gave out food to people out of work.
政府向失業者分發食品。
He gave out that the president was dead.
他宣布說總統去世了。
It was feared that food supplies would give out before the besieged town could be relieved.
都害怕在那城市解圍之前斷了糧。
Both the man and the horse gave out after the long ride.
趕了很長一段路後，人馬俱乏。