That depends on whether you're looking for interchangeability in modern usage or in their historical usage. Today, they are both just generic terms for a religious war, differing only in the originating religion and the cultural baggage that comes with it. In this light, jihad makes sense with the desert setting of Arrakis, but crusade is more relatable to western audiences.

But you came to r/askhistorians, so here's the historical answer: no. Very much no.

Obviously, each term comes from a different religious background, each of which has its own concept of righteous religious warfare.

We can start with the words themselves: "jihad" literally means "struggle," and can refer to any conflict pursued in the name of God, whether a military campaign against non-muslims or a deeply personal wrangling with doubt or sin. The translation of this concept into warfare is comparatively straightforward compared to "crusade," which derives from "cruciatus," classically referring to someone crucified but by the 11th century more abstractly referring to one "marked with" or "bearing the cross." This refers to the rather queer concept which birthed crusades: the idea of an armed pilgrimage.

See, carving out Latin Christian states from the Levant was not the necessary outcome of the First Crusade. Conquest of some sort was inevitable, but many expected lands to simply be returned to the Eastern Roman Empire. The precise ownership wasn't the point - the campaign was launched first and foremost to secure pilgrimage routes, something essential to medieval piety, and it was to be spearheaded by a armed pilgrimage which would clear the way... somehow. After friction with Constantinople, this meant the Crusader States, most especially the Kingdom of Jerusalem.

As the vanguard of pilgrimage, crusaders were seen as 'taking up the cross' in following the path of Jesus of Nazareth and accordingly marked themselves with visible crosses. Thus, cruciatus, crusader, crusade. Pilgrims first, and religious conquerors (against prior Christian custom) second. Campaigns elsewhere would play fast and loose with the concept (especially the Northern Crusades), but the rule, contrary to the imagination of most people commenting 'Deus Vult' on the internet, was restoration of past Christian rule and/or the "liberty of the Church."

Jihad pursued as a military campaign, however, is essentially about conquest, or, to be more accurate, submission. The historical principle is that there is one ultimate God and one ultimate religion which must dominate, not merely through the spiritual allegiance of the populace, but through a hybrid spiritual-temporal authority expressed in the Caliph. While these could be defensive in structure (preserving the place of Islam in a threatened land), they were often unapologetically offensive campaigns to secure the submission of new lands to Islam.

Of course, we shouldn't fall into the caricature that exists in some imaginations: mad fanatics proselytizing by the sword, convert-or-die, etc., as through al-Baghdadi's attempt to establish a caliphate years ago was faithful to the original. If that were the case, Syria and Egypt would not still be 10% Christian today, well after a millennium of Islamic rule in one form or another. It's notable that in the latter case, Miaphysite Christians supported the takeover as liberation from their Chalcedonian (whether you want to call them Catholic or Orthodox) Roman rulers.

But the fact remains that classical, military jihad was offensively-minded and expansionistic, with the express purpose of subduing additional lands into the Islamic world. They also occurred in a frequency that far surpassed the crusading campaigns of even the same periods - by some estimates (although this kind of thing is difficult to measure with certainty), they may account for nearly half of all wars launched on religious grounds.

In contrast, crusades were classically reactive, whether to curtailment of pilgrimage rights, the outbreak of some organized heresy, or to raiding from a pagan neighbor, occurred with far less frequency, and generally pursued subjugation as a means to another goal.

So, let's revisit Dune: Muad'dib, Paul Atreides, is at the helm of a vast campaign of religious conquest as his followers subdue the known universe to his temporal and spiritual authority. From our past and the theology of each religion, it seems clear that jihad is the appropriate term historically and not merely a cultural reference to the desert setting of Arrakis, while crusade is an awkward fit unless you adopt the modern, undifferentiated usage.