I have a question for basic operating with certificates in emails and pdfs. Im familiar with public key cryptography.

The scenario:

In my scenario I want to send a confidential email to a person A from a server B.

My understanding (no certificates):

Keypair 1: private key AA, public key AB

Keypair 2: private key BA, public key BB

Keypair 1 is generated on the server. Private key AA stays on the server, Public key AB is transfered to Person A. Keypair 2 is generated on the client. Private key BA stays, public key BB is tranfered to the server.

Now I sign the message with private key AA and encrypt it with public key BB on the server B. Person A verifies the signature with public key AB, and decrypts it with private key BA.

Question:

I want to translate this scenario of using certificates. What confuses me is who holds which certificate what inside these certificates and types. Any help is appreciated!

Thanks in advance. If something is unclear please let me know.

EDIT:

Thanks to all for the nice answers. Cant decide which I should give the "thumb up". Love the star wars example :).