Hybrid Identity Authentication & Entra Connect

Hybrid identity model & directory synchronisation is the most common for enterprise users
Directory synchronisation allows updates to AD DS to synchronise with the Entra ID
AD DS identities are synchronised with Microsoft 365 and users are managed on-prem
Managed Authentication
Password Hash Synchronisation (PHS) (Recommended)
Entra ID handles authentication using a locally hashed password
Password hashes are synchronised out from AD DS to Entra ID so that users have the same password
Pass-Through Authentication (PTA)
Entra ID sends the credentials to an on-prem software agent to be authenticated by AD DS 
Federated Authentication
Federated Authentication - Entra ID redirects the client's authentication request to another identity provider
Primarily for large enterprises with more complex requirements
Users have the same password on-prem and in the cloud and do not have to sign in again to use 365
Supports additional requirements such as smartcards or third party MFA