delusion implies belief that something is true which is not

illusion is knowing it is not true but experienced as if it is true

All my terms, unless otherwise specifically noted are using native English word senses you can find in a dictionary.

"lie" for example is defined by its word sense.. i.e., things people will call a lie. However, in the Internet Court of Lies it is defined in set theory terms as NOT the truth, the whole truth, and nothing but the truth. I.e., defined in terms of the word sense for "truth". This definition of lie is universal and matches the word sense use of the term fairly well.