这两个短语都表示散发，发出之意，一般可以换用，但侧重点有所不同。 give off通常用来表示散发，发出某种气体或气味。如： Boiling water gives off steams. 开水散发出蒸汽。 This milk must be bad, for it is giving off a nasty smell. 牛奶一定变质了，因为它散发出一种令人恶心的气味。
The chimney no longer gives off volumes of waste gas into the atmosphere, as protective filters are being used. 加装了防护过滤器以后，这烟囱已不再向空中散发成股的废气了。 give out 则通常用来表示散发某种光，声，热，信号等物理现象。此外，它还可以表示分发，宣布，耗尽等现象。如： The leaves gave out a whirring sound. 树叶发出沙沙声。
The sun gives out light and heat to the earth. 太阳向地球发出光和热。 The ship gave out radio signals for help. 船发出无线电信号求助。 The government gave out food to people out of work. 政府向失业者分发食品。 He gave out that the president was dead. 他宣布说总统去世了。
It was feared that food supplies would give out before the besieged town could be relieved. 都害怕在那城市解围之前断了粮。 Both the man and the horse gave out after the long ride. 赶了很长一段路后，人马俱乏。