I'll take a somewhat different, and perhaps more interesting, example than the Ottomans (who used religion extensively as well).
France expanded fairly consistently throughout the period, but used a variety of justifications for that expansion.
The initial situation, as with EU4, was English lands in France, followed by reclaiming Burgundy (or at least the French portion). The Hundred Years War went back to the Middle Ages and the situation where the King of England was also feudal lord of various places in France, and thus theoretically a vassal owing homage for those titles (but not for others; the Duke of Aquitaine was a vassal of the King of France, but the King of England wasn't, even though the King of England and the Duke of Aquitaine happened to be the same person). This led to various disputes (for example, a vassal of England in Aquitaine might have a dispute with the English king, and appeal to the King of France to intervene as legal overlord of Aquitaine, while the King of England would tell him to get stuffed, providing an excuse for war). The King of France could then claim that the "Duke of Aquitaine" was being a disloyal vassal, and revoke his title, providing an excuse to try and conquer the English-held lands.
Burgundy was an inheritance situation. Burgundy was officially a vassal of France, but in practice was independent. Nevertheless, when the Duke of Burgundy died without male heir, France claimed most of Burgundy due to the extinction of the house in the male line, while Austria claimed the inheritance through marriage to the daughter of the last Duke. They eventually agreed on the division in-game, but both sides continued to try and retake the whole duchy in various wars over the next couple of centuries.
Meanwhile, the French king married the last duchess of Brittany and brought that duchy into his kingdom that way, while the death of the King of Naples gave an opportunity to claim that throne (since the King of France was descended from a previous ruler in the female line), supported by a previous offer from a former Pope (who had been feuding with the King of Naples at the time and offered to give Naples to France instead), leading to the Italian Wars.
You had similar situations in other French expansions, with various ambiguous succession disputes and old treaties being cited as justification for conquest. For example, the French conquest of much of Flanders and the Low Countries was due to a dispute over the dowry of a Spanish Princess who had married the King of France (Spain was bankrupt at the time and never paid the dowry, so the French claimed her share of the Spanish Netherlands instead, leading to a war). Likewise, the War of the League of Augsburg started when the French invaded the Palatinate under the excuse that the daughter of the last Elector Palatine was married to a French prince, and thus France needed to protect her rights (and incidentally bring the Palatinate under French control).
Colonial territories tended to be much more open to straight out claims by Right of Conquest, since they were viewed as having been previously occupied by non-Europeans, whose claims were easier to ignore (although they could still be used at times when an excuse was needed, arguing that e.g. this tribe had once sworn fealty to Spain, and thus all their land was rightfully Spanish). So swapping colonies or taking them from others was much easier to justify.
After the French Revolution, of course, Revolutionary France claimed it was liberating the various places it conquered from the tyrannical rule of monarchs (sometimes establishing puppet states, sometimes annexing them outright to the Republic).
