A small subset of furries, called “therians,” go beyond the interest in developing a fursona and believe they are spiritually connected to animals, are less than 100 per-cent human, are an animal trapped in a human body, or were an animal in a former life (Gerbasi et al., 2008).
There's also the dissenting opinion that therians are a separate group from furries, an opinion perpetuated both by therians and "normal" furries, but it's generally the minority opinion, so for all intents and purposes, this is accurate.