Nārāyaṇa-daśā is a specialized application of cara-rāśi-daśā where the starting rāśi is the ārūḍha-lagna (AL) rather than the lagna. The computational rules are identical to cara-daśā; only the start-point changes. Interpretively, this matters: cara-daśā from lagna tracks the inner-life trajectory; nārāyaṇa-daśā from AL tracks the outer-life / public-image trajectory.
Practical use: when analyzing career-recognition events, public-emergence moments, or any signification tied to how-the-world-perceives-you, nārāyaṇa-daśā can outperform cara-daśā-from-lagna. When the two diverge in a chart, the classical interpretation reads it as a misalignment between the inner-self and the public-self — sometimes generative, sometimes uncomfortable.