Short answer:

• Parrushan Parva (the holy month of reflection and fasting) is a Jain observance. It is part of Shwetambar practice and is about increasing spiritual discipline during Kartik month, with darshan, pravachan, and fasting.
• Ganeshotsav is a Hindu festival honoring Lord Ganesha. It is not a Jain ritual or canonical festival.
• Dash Lakshana Parva refers to the ten auspicious virtues/characteristics described in Jain scriptures as qualities of a spiritually realized being (kevali/ten virtuous traits). It is a Jain doctrinal concept.

How they relate (clear, Jain-centered view):

• There is no doctrinal or ritual equivalence between Parrushan Parva and Ganeshotsav. Any overlap is cultural or seasonal, not a shared Jain practice.
• Dash Lakshana Parva is a Jain teaching about the ideal virtues of a liberated soul. It is a scholarly or scriptural reference within Jainism and does not originate from or connect to Ganeshotsav. Parrushan Parva, while a core Jain practice, does not depend on the Dash Lakshana Parva as its foundation; Parrushan emphasizes personal tapas (austerity), reflection, and devotion to Tirthankaras.

Differences between Digambar and Shwetambar:

• Parrushan Parva is observed by both Digambar and Shwetambar communities, though rituals, temple practices, and dates may vary slightly by region.
• The Dash Lakshana Parva is a concept discussed in Jain scriptures and commentaries; interpretations of the ten Lakshanas can have slight differences in Digambar vs. Shwetambar exegesis, but the core idea remains the same: it outlines the virtuous qualities of a liberated being.
• Ganeshotsav has no official status in Jain practice in either tradition.

If you’d like, I can share the exact Jain scriptural references (as preserved in Digambar and Shwetambar sources) for Parrushan Parva and for the ten Lakshanas, with a simple, authentic arth (meaning).