The dividing line is whose money moves
If the firm's own capital is at risk, the business is a proprietary operation: no client assets, no instructions from third parties, no obligation to return anything to anyone. If customers can deposit, hold or withdraw value, the business is holding other people's money and becomes a custody, exchange or portfolio-management profile, whatever it is called.
Everything downstream follows that line: whether a licence or registration is required, whether client funds must be segregated, which regulators can act against you, and which institutions are willing to hold the relationship. Establish which side of it you are on before a single form is filled in.