Historically, raise, from Old Norse, was reserved for crops, meaning literally to make higher, and rear, from Old English, was reserved for bringing up children. Raise wasn’t applied to animals until the 1700s, according to the History of English Podcast, from where its use evolved into a synonym of rear.
It is now standard and far more common in both American and British English to raise children than to rear them, and phrases like born and raised are so ubiquitous that born and reared sounds humorously stilted. Consider both words appropriate for children and animals, though understand that raise will feel more natural to most readers.