Both mean statement in english. Can someone explain to me what the difference between Äußerung and Aussage?
Äußerung = a concrete statement made by a particular speaker at a certain point in time.
Aussage = the logical proposition that was expressed by it.
In a parlimentary debate, lots of speakers can make many utterances (Äußerung), most of which convey the same proposition (Aussage). Conversely, a skilled diplomat might make a single finely crafted utterance and appear to mean slightly different propositions to both parties in a negotiation.
Äußerung translates to utterance (as in 'something uttered; a word or words uttered; a cry, animal's call, or the like.'1) while Aussage translates to proposition, the difference is the same as in english.
Sometimes this border does not seem to be so sharp and Äußerung is used in the meaning 'statement, proposition' as well. This might be the source of your confusion.