Which certificate do you need?
Four questions. The logic: a succession certificate (District Court, Section 372) is for debts and securities when there is no will. A will means probate instead. A legal-heir certificate (Tahsildar) is for government pension, gratuity and dues — and only in the states that issue one. Immovable property needs mutation, not a succession certificate.
The rule, in one paragraph
Under the Indian Succession Act, 1925, a succession certificate is granted by the District Judge where the deceased ordinarily resided, on a petition under Section 372. It covers debts and securities only — bank deposits, shares, PF, insurance. Section 370 bars a succession certificate where the deceased left a valid will: then the route is probate (or letters of administration with the will annexed). A legal-heir certificate is a different document, issued by the Tahsildar / Revenue Department in the states that issue one, and is used mainly for government pension, gratuity and dues. Immovable property is transferred by mutation (with probate, if there is a will) — a succession certificate does not transfer title to it.
Sources: Indian Succession Act, 1925 — India Code, BankBazaar — Succession Certificate in India, QuickCompany — Succession Certificate: Eligibility & Procedure