Plain version: think of three doors into Medicare: age, disability, and two specific diseases. Each door has its own start date.
Age 65: citizens and legal residents aged 65 or older.
Someone 65 or older who is not otherwise entitled to Part A can still enroll in Part B if a U.S. resident and either a citizen or a lawful permanent resident who has lived here continuously for the five years before applying.
Taking early Social Security retirement benefits at 62 does not create Medicare eligibility; the person waits until 65.
Social Security Disability (SSDI): Medicare based on disability starts with the 25th month of entitlement to disability benefits. That is the "two-year wait." Example: entitled to disability benefits in March 2024 (month 1), so Part A begins in March 2026 (month 25).
Two diseases with special timing:
Amyotrophic lateral sclerosis (ALS, "Lou Gehrig's disease"): the 24-month wait is waived. Medicare begins with the first month of disability benefits.
End-stage renal disease (ESRD): entitlement generally begins on the first day of the third month after the month regular dialysis starts. Dialysis that starts in June leads to Medicare on September 1. It can start earlier in cases such as self-dialysis training, and ESRD does not require 24 months of disability benefits.