The outcome is similar, but the system is different.
In India, markets are depository-first (NSDL/CDSL). Shares are held in a demat account in your name, and brokers act as intermediaries.
In the US, markets are brokerage-account-centric. The brokerage account itself is the primary container for assets.
Because of this difference, US transfers move assets between brokerage accounts rather than between depositories, and are handled through systems like ACAT, DTC, or DRS.