Ramanuja qualified non-dualism turns on one image. Souls and the material world stand to God as a body stands to the self that inhabits it: really distinct, wholly dependent, incapable of existing or acting apart, and yet not a second thing alongside him. That lets the tradition say the reality is one without saying the individual soul is an illusion, which is exactly what it accuses the Advaita reading of doing. Three realities are counted, God, souls and matter, and the last two are the body of the first.
The route to God is bhakti sustained over a lifetime, and beside it prapatti, self-surrender, offered once and completely by someone who cannot manage the longer discipline. What surrender means, and how much the person contributes to it, is where the tradition divided in the centuries after Ramanuja.
The two schools that resulted are the Vadakalai, the northern, and the Tenkalai, the southern, and the standard illustration is a pair of animals. The monkey infant grips its mother, so some effort of the soul is required; the kitten is carried in the mother mouth and does nothing at all, so grace is entirely unearned. Around this cluster a list of doctrinal differences, along with divergent positions on the standing of the Sanskrit and Tamil canons and on the role of the goddess. The split is institutional as well as theological, with separate lineages, separate liturgical usages and long-running disputes over the conduct of worship in shared temples.