[lingben]

What you write is correct, except for this part:

The IRGC is not a 'special wing' of the Iranian military. They are a completely separate organization which has no equivalency in Western societies or defense departments.

The IRGC is tasked with protecting and spreading Khomeini's brand of Islamic theocracy throughout the world. This is why you see Iranian proxies in Yemen, Nigeria, Lebanon, Gaza, Syria, etc.

The Iranian military is tasked with protecting the Iranian nation and people. The military is a lower priority and less funded that IRGC, especially since the IRGC is a major actor in Iran's economy via various bonyads.