The answer comes from section 2.3 Client Authentication.
If the client type is confidential, the client and authorization server establish a client authentication method suitable for the security requirements of the authorization server. The authorization server MAY accept any form of client authentication meeting its security requirements.
Confidential clients are typically issued (or establish) a set of client credentials used for authenticating with the authorization server (e.g., password, public/private key pair).
The authorization server MAY establish a client authentication method with public clients. However, the authorization server MUST NOT rely on public client authentication for the purpose of identifying the client.
Section 2.1 Client Types
OAuth defines two client types, based on their ability to authenticate
securely with the authorization server (i.e., ability to maintain the
confidentiality of their client credentials):
confidential
Clients capable of maintaining the confidentiality of their
credentials (e.g., client implemented on a secure server with
restricted access to the client credentials), or capable of secure
client authentication using other means.
public
Clients incapable of maintaining the confidentiality of their
credentials (e.g., clients executing on the device used by the
resource owner, such as an installed native application or a web
browser-based application), and incapable of secure client
authentication via any other means.
Summary
The requirement for an authorization header is determined by the authorization server and is implementation specific.