What is the difference between atheism and irreligion?

The main difference is that one refers to the existence of (a) God, and the other refers to the practice of (a) Religion.


Atheism is quite simply the lack of a belief in a god, theism being a belief in a God, and the prefix "a-" meaning "without" .
e.g. Gnostic/Mystical Knowledge v Agnostic/without Mystical Knowledge, or Moral meaning a system of ethics v Amoral meaning without a system of ethics.

Then we have immoral which means against the system of ethics. And antitheism which is against the existence of (a) God.

Irreligious means indifferent to or against religion. The prefix "ir-" means "not" as in irrelevant (not relevant). So irreligious can mean simply not religious, however actual use of the word is more often of the second hostile type: against religion.

It is irreligious (against the religion, disrespectful of the religion, or hostile to the the religion) to do something the religion disapproves of. In this way, "irreligious" is more akin to immoral than amoral.

A religion may find atheism to be an irreligious position.

Definition

Irreligion is defined as a rejection of religion, but whether it is distinct from lack of religion is disputed. The Encyclopedia of religion and society defines it as the "rejection of religion in general or any of its more specific organized forms, as distinct from absence of religion"; while the Oxford English dictionary defines it as want of religion; hostility to or disregard of religious principles; irreligious conduct; and the Merriam Webster dictionary defines it as "neglectful of religion : lacking religious emotions, doctrines, or practices".

https://en.wikipedia.org/wiki/Irreligion

I think more simply put, Atheism is a rejection of God, while Irreligion is a rejection of religion.
the difference may seem minor on the surface however there are some that posit that Atheism is a religion.

"I'm not religious. I'm an atheist." This is a common statement today, especially in the West, but it is at heart an oxymoron. While atheism does not look like Christianity or Islam, the two largest religions in the world, atheism is a religion. This, of course, is a statement that has earned ridicule, slander and rage more than once. Many atheists will argue that the very definition of atheism is "non-religious." While it is true that atheists do not believe in God, that does not mean that they are not religious.

https://www.beliefnet.com/faiths/secular-philosophies/is-atheism-a-religion.aspx