A modeling agency represents talent and tries to place that talent on paid work. A casting company is usually working from the other side of the table: it helps a production or client find people for a brief. Sending the same message to both as if they were interchangeable is an easy way to look unprepared.
A “mother agency” is a relationship, not a magic label. In international modeling it commonly refers to the agency that develops a model and may coordinate placements with agencies in other markets. The exact commercial arrangement belongs in the contract, not in assumptions.
For a first contact, identify what the organization actually is, use its official application channel, and adapt what you send. If it is an agency, you are asking about representation. If it is a casting company, you are usually responding to a role or joining a casting pool.