That was not just the West's portrait, but Da'esh' own self-portrait as well. They focused their own recruiting on extremist madmen who were single-mindedly committed to their violent interpretation of Islam - hardly an exercise in peaceful state-building.
Partly because of this conflation the whole narrative (heavily sponsored by oil money of course) have kept blind Western elites for very long time, especially in Europe, where they only start to understand that worship places with heavy foreign aid inflow are not necessarily harmless community centers, and "religious liberties" must have strict bounds to be classified as so.
Wahhabist is not really actually something anyone would refer to themselves as. It seems to refer to really any Muslim group that has some links to Saudi Arabia which is a key player in the geopolitical arena of the Middle East.
Salafi is really anyone that would like to emulate the companions of the Prophet Muhammad and the immediate generation thereafter, Salaf meaning ancestors. This actually would have no more outward political ramifications than what has already been in Islam from the beginning, Islam is meant to encompass governance whether one would agree with that or not, it's part of the religion. Salafi would nearly exclusively refer to the Quran and Hadiths as their source.
I have seen the term thrown around as a label for individuals that have done terrible things but by all accounts were not even remotely close adherents to salafi like doctrine. It's not a political group it's more of a doctrine.
Not every religion is a religion, that is.
My understanding is that Da'esh governance (and recruitment, to some extent) was not dissimilar to early Nazi governance. Yes, they managed their state, but within an ideology based on an imaginary past, on permanent internal violence against real and imaginary enemies of the state, total war against foreign inferiors, and of course genocide (against Yezedi in the case of Daesh).
To add to the parallel, the economy of both states were also, to a large extent, based on plunder, and both nations were born from the ashes of scars of the partial destruction of their country at the hands of foreign powers and a revenge fantasy against said powers and the imaginary conspiracy that caused the fall.
There are also many differences, of course. But my take on it is that there are enough similarities that the world (including myself) not seeing it coming is a failure. Also, yeah, both nazis and da'esh had a mostly working state, but at what cost?
I'm not talking about rallying people to cause but rather ensuring municipal activity is happening regularly and that one is generating enough revenue to sustain these activities. Arguably Nazi Germany never really had the latter though, and instead needed to borrow heavily and go to war.
These points seemed that gone over the heads of most here who defaulted to the "oh look, bogeymen that we are all so superior to"