Learn English – the difference between happens with and happens to

A delusion is a strongly held belief even when there is strong evidence that the belief is false.

An illusion deceives or misleads someone about the true nature of something. Magicians are often called illusionists because they mislead us into believing that something impossible has happened. Most of the audience however is not deluded into believing that the magician actually performed real magic.

For example:

"The positioning of the mirrors gave the illusion that the room was much larger than it actually was."

"If we could dispel the delusion that Engineering requires a passion for mathematics, we might see more women studying it."

There's not really any difference in meaning, only in emphasis.

When you add the word single, you are intensifying the emotion with which something is said, whether that be frustration (as in the first example) or elation (as in the latter):

Every time we plan a picnic, it rains.
Every single time we plan a picnic, it rains.

Every time I go on a date with Carol, I don't want the night to end.
Every single time I go on a date with Carol, I don't want the night to end.