No visa for either country. What you do need is the right ID, a guide on most routes and a few permits. Here are the rules for Indian citizens, each linked to the official page.
Nepal
Everest, Annapurna, Langtang and Manaslu, plus Gosainkunda, Muktinath and Pathibhara Devi for pilgrims. No visa for Indians.
Rules for Indian citizens
Entry documents
No visa. Carry a valid Indian passport or an Election Commission voter ID.
Over 65: a PAN card, driving licence or ration card with photo also works. Under 18: an ID card from the school principal.
Since 31 March 2023, the main protected-area routes (Everest, Langtang and Gosainkunda, Annapurna, Manaslu, Mustang, Kanchenjunga, Makalu, Dolpo and others) need a licensed guide and a TIMS card issued by a trekking agency.
TIMS fee for SAARC citizens, including Indians: NPR 1,000.
No official page exempts Indians from the guide rule. Plan on a guide and confirm with your agency.
Upper Mustang, Manaslu, Tsum, Nar Phu, Dolpo, Kanchenjunga and Humla need a restricted-area permit, issued only through a registered trekking agency and priced in US dollars.
Upper Mustang: USD 50 per person per day. Manaslu: USD 100 a week in Sep–Nov, USD 75 a week in Dec–Aug.