Ka and ba are easily confused by a reader meeting Egyptian religion for the first time, since both are commonly translated with the vague English word "soul," but the ancient system distinguishes them by function rather than treating them as synonyms or as two names for one thing. The ka is created at birth, is closely bound to the physical body and its sustenance, and is generally described as staying at or near the tomb, waiting to receive its offerings. The ba is specifically the part credited with personality, individuality and, crucially, mobility, the aspect able to travel and to represent the deceased's continuing agency in the world.
The two are not rivals for the title of "the real soul"; Egyptian religion treats a person as composed of multiple genuinely distinct elements, ka, ba, akh, the shadow and the name among them, each contributing a different capacity, and personhood as a whole depending on all of them functioning together, in life and, through ritual, after death as well. Losing any one of them, in the logic of the funerary texts, was a real danger, not a philosophical nicety.
What ties ka and ba together most directly is the akh, the transfigured, effective spirit that Egyptian belief holds results from their successful reunion, achieved through the correct performance of funerary ritual, the recitation of the right spells, and the preservation of the body as an intact, identifiable anchor. A ba that could not find its ka, or a ka left with no ba to reunite with, was understood to leave the deceased incomplete, unable to become an akh and share in the afterlife the whole funerary system was built to secure.