Ahahah oh boy. Okay there's enough to be said about cross race interactions and relations in piaj worldbuilding to fill an encyclopedia, which it in fact has been, so I'll.....try to not make this too long. Try being the operative word.
1. Skywing elves have three main types of society: the nomad clans, the cities, and the temples. These view each other differently and can have drastically variable cultures. Nomad clans will interact with a wide variety of other races of elf and in many cases will dominate other races' impressions of what Skywing elves are like; given how drastically the clans vary in their culture and outlook, this means elves in different parts of Xadia will have very different impressions about Skywings. Temple elves are viewed as more serious, but also potentially annoyingly distant from the troubles of the world; city elves are viewed as generally sensible but pretty weird, given their cultural ideas have very definite impacts on their architecture and way of life. On the whole, almost all Skywing elves are social and community-focused to a degree that can disturb other races, particularly Moonshadow elves, who have a high level of investment in their communities but are considerably more private with their personal and inner lives.
2. Sunfire elves are very disciplined and organised, with some of the most advanced infrastructure and the largest cities in Xadia. They place heavy emphasis on military service, to an extent that may make other races of elf find them unusually militant and warlike. Despite this, many Sunfire cities are some of the most cosmopolitan there are, and will host higher numbers of other races than you tend to get in other races' settlements.
3. Earthblood settlements and society vary considerably, but it is well known that many of their greatest cities are underground in vast cave systems. This suits the Earthblood elves perfectly well, but is considered unthinkable by Sunfire, Moonshadow, and Skywing elves. All three races would grow very sick and weak from magic deprivation should they live underground, with the possible exception of Sunfires, if they were close enough to active magma flow. Skywing elves in particular find the idea of living underground to be anathema, and wholly unnatural. It is a widespread cultural attitude among Skywing elves that to live where the Sky magic cannot move - in the Barren Air - is to become cursed and die. Most will not extend this attitude towards the Earthblood elves who live underground, but the more religious and intolerant will; in some of the nomad clans, Earthblood elves will be referred to with honorific prefixes ranging from mildly disrespectful to the worst of all: 'sha'; cursed. This is pretty uncommon though.
4. Most Moonshadow elves live in seclusion and rarely interact with elves outside their settlements. Many of them hide their towns and villages, and emphatically do not welcome strangers. The majority of their contact with other races is generally for trade of luxury goods, which often ends up being with Skywing nomad clans. Given that few nomad clans have a culture requiring rigid emotional disclipline of the sort that Moonshadow elves value, they often end up viewing their trading partners in a relatively negative light. They respect Sunfire elves for their military disclipline and their efficiency, but dislike their overt gaudiness and directness of methods. Moonshadow elves favour precision over brute force, and 'brute force' is certainly how they tend to view the Sunfire militaries. Meanwhile, Moonshadow elves are pretty widely held as xenophobic, distrustful, unfriendly, and somewhat stuck-up by other races of elf. Sunfire elves, meanwhile, do respect their discipline and martial prowess.
5. I've basically completely refrained from worldbuilding Tidebound elves until there's more info on them so can't really say anything there.