That’s a really good question, I have never really thought about the differences.
Intent and desire are different and yet both are needed and used along the way.
With regards to actualism intent will usually refer to a sincere intent or pure intent.
The difference between sincere intent and pure intent is more a difference in degree and not kind (although they are referring to 2 different things), hopefully my Pure intent diagram somewhat demonstrates this - Depictions of Pure intent
As you can see from the very beginning it is the experience of purity which ‘trickles down’ and at the most basic level expresses itself as a sincere intent - “there must be more to life than this, I will find a way”.
With more PCEs and more time feeling happy and harmless one eventually develops a connection to the purity of the actual, then it is not as much ‘trickling down’ as a highway that has been opened up between ones state of naiveté and the perfection and purity of the actual world.
In terms of desire, a burning passion to become free. This seems to be all to do with using whatever one has at ones disposal.
As in ‘I’ cannot get around the fact that ‘I’ a passionate entity, the best that ‘I’ can do is direct all of ‘my’ passionate energy of desire towards the goal of becoming free.
It seems here is where the experiences of purity and desire work together, it is the experience of the utter purity and perfection of the actual world which makes one want it like one has never wanted anything else before.
Then it is the desire which is pushing one from the back and the pure intent which is pulling one from the front.