A securities firm is a securities company whose main businesses are brokerage (customers buy and sell through it), self-operated (buy and sell by oneself), underwriting (help others sell securities), and asset management (help others operate).
The main business of the fund is to manage money for customers (help people operate).
Institutions in the narrow sense refer to funds, and institutions in the broad sense refer to investment institutions such as securities firms, funds, and insurance companies.