Do different parts of india celebrate the festival for different reasons? I have heard that for Bengalis Durga puja signifies Durga returning to her parents' home from Kailash to spend time with them.
This answer is only with reference to Durga Puja - specifically in Bengal. The answer is sourced from Wikipedia and also other sources from the net. No scriptural reference is available with me for the legend.
The Akaal Bodhan Sharadiya Durgostab celebrated in Bengal is the most important event in the Bengali calendar - though Bengalis have their festivals throughout the year, it is said "Baro Mashe tero Porbon" i.e in twelve months thirteen festivals.
Sharadiya (Autumn) Durgostab also coincides with Dusshera - Dasa Hara - the commonly held belief that Sri Rama slew Ravaana on this day. Bengal also celebrates Basanti (Spring) Durgotsab. Basanti Durga rides an ass, while Sharadiya Durga is the Sherawali slayer of Mahishasura.
On Mahalaya Day, the eve of Sharadiya Navaratri, at dawn Bengal resounds with the sound of Chandi Paat, the recitation of the battle of Devi Durga with the demonic hordes led by Mahishasura. The belief is the battle lasted six days and mahishasura was killed on the evening / night of Panchami.
Tired of the battle and wanting to recuperate, Maa Durga, with the permission of Her consort Lord Shiva comes down to the plains of Bharatavarsha, Her parents house along with ther children Lakshmi, Saraswati, Ganesh and Kartick. She arrives on Sashti day and remains with her parents for four days - Sahsti, Saptami, Ashtami and Navami departing for Her husband's abode on the afternoon/ evening of Dashami day. To herald Her departure - Neelkanta Pakhi - Blue birds are freed who are supposed to go to Mount Kailash to inform Lord Shiva about the return of Durga and Her family.
how far this belief will stand scrutiny of the scriptures is a moot point. Srimad Devi Puranam (Bhagavatam) states that Lakshmi and Saraswati are forms of Adi Shakti herself, who took on these forms to live with Vishnu and Brahma. There is no mention of them being the daughters of Adi Shakti (Kali / Parvati)