In terms of culture, how were they different? Were the religions the same? I’m just curious as I’ve read about them and would like to know more.
Okay, something in my wheelhouse. Not often that comes up, thanks for asking!
So the scope of your question, for those unfamiliar, is broad both temporally and spatially. The Chavin phenomenon extended from 950 BC to sometime in the 5th century BC (due to problems with radiocarbon dating during that time period the timing is a bit coarse). Meanwhile, the Nasca and Moche societies lived during the early centuries AD. Each of those societies can trace some parts of their religions and culture to the Chavin religion in some way, so it's best if I take it stepwise and begin with what Chavin was.
It's important to note that Chavin was far from the first society with monumental architecture, stone sculpture, or complex iconography. Mound-building had been taking place on the north, north-central, and central coast of Peru for well over a millennium at this point; this was undertaken by sedentary societies which seem to have communally organized their labor in the common effort of building monumental ritual structures and complexes, perhaps even for local/regional pilgrimage. Likewise we know now that on the eastern slopes, there was ritual architecture at sites on the fringes of Amazonia, in places like Santa Ana-La Florida in southern Ecuador. Some form of commodity exchange was taking place across regions for valuable and spiritually significant materials like red Spondylus shell (which only grows off the shores of far, far northern Peru and more consistently in Ecuadorian waters). And in the northern highlands, the Kotosh Religious Tradition saw communities building and re-building temples for their community on the same spot for centuries at a time, and illustrating some of the early manifestations we have of deep-seated Andean principles like duality and the presence of an "other" world, a sacred plane accessed via shamanic practice for the health of the community.
Chavin entered into this at a fascinating point, when many coastal religious centers were being abandoned; in the search for new meaning and understanding of the world, it seems that the religion of the Chavin, as enshrined in its primary center of Chavin de Huantar, found purchase in the hearts and minds of Andeans throughout the coast, highlands, and eastern flanks. Combining coastal iconographic methods with selvatic subjects like jaguars, caymans, and harpy eagles (here is one actual size - this isn't me but I use this guy's photo to show how huge they are!), and also synthesizing architectural canons from across the coast and highlands. Chavin de Huantar saw a massive influx of pilgrims visiting the site for consultations with their gods, including the idol known today as the Lanzon. Much of this would have been done with the aid of hallucinogenic drugs obtained from the jungle, in order to enter the spiritual plane and contend with the deity for its aid (with the help of Chavin's religious attendants, of course).
Now, some would argue that Chavin was some kind of theocratic state; however the archaeological data we have and the diversity of sites in the Chavin sphere (each with variable expressions of that style and logic) indicate to me and other scholars that Chavin is best understood primarily as a religion. Examining most of their cult centers, then, is less like excavating a city and more often like excavating a cathedral. These are sacred spaces which conform to distinctive organizational principles but which also contend with local manifestations and expressions, and each of these centers (Campanayuq Rumi, Atalla, Chawin Punta, Pacopampa, Kuntur Wasi) have their own flair. It's a bit like comparing Christian cathedrals from Spain, France, Germany, Italy...these spaces are often organized the same and in service to the same deity, but local architectural traditions also leave their mark to the trained eye.
The exception to this pattern is...Chavin de Huantar. In addition to the cult center, Chavin de Huantar maintained an elite district behind the complex, and towns on the other side of each of its two rivers (the sacred center sits at a confluence of two rivers). Estimates of the town's population sit at about 3-5,000 people during the later phase of Chavin's occupation, the Janabarriu phase (ca. 700-500 BC and perhaps as late as 400 BC). Of all those pilgrims, some of them evidently stayed in the valley, setting up shop as farmers, craftspeople and various specialists alongside the exiting populations of llama herders which lived there for centuries beforehand. Chavin is a strange inflection point in the prehistory of the Andes, a sort of "end of the beginning". I say this because during this later phase of Chavin's religious expression, archaeologists see the emergence of social stratification with burials of an elite with religious authority. The expansion of trade routes, llama caravanning, and all the commodities suddenly making its way throughout this religious sphere - cinnabar from Huancavelica (Atalla), obsidian from Ayacucho (Campanayuq Rumi), Spondylus being imported from Ecuador and worked in Peru, rapid advancements in metallurgical artistry - all of this eventually coalesced around the religious authorities of the site who began to be ascribed their social status rather than earning it through their lives. They began being buried with gold and rare pigments; during their lives they were able to secure the most tender llama meat, leaving the older, tougher individuals to the people of the town. This pattern of stratification manifested particularly strongly in the primary center as well as at sites like Pacopampa and Kuntur Wasi farther to the north. Yet while this arrangement of elite legitimacy, this deal with the hierarchical devil, never really went away post-Chavin, it didn't last long for the Chavin religion itself. Sometime in the fifth century (or perhaps during its length), faith in Chavin religion precipitously declined, and many regions cut ties with each other and balkanized into various regions. The following few centuries saw numerous bellicose societies develop, such as the Salinar on the north coast, favoring strong warriors (male or female) and featuring a massive uptick in evidence of skeletal trauma from clubs and sling stones (cranial edema, ouch).
In a reply I'll get to where Nasca and Moche each fit into this trajectory, but I needed to set the stage before we could discuss what made each of them different! Stay tuned, I'll have it up in a little bit below this post.
Regarding Andean prehistory in general:
Quilter, Jeffrey, 2014. The Ancient Central Andes. Routledge, London.
For early Andean monumental prehistory up to and including Chavin:
Burger, Richard L., 1992. Chavin and the Origins of Andean Civilization. Thames and Hudson, New York and London.