JID and Contacts
JID - Jabber ID or XMPP Account
The "JID" (Jabber ID) or XMPP Account is the XMPP chat address of a user and is similar to an email address: "user_name@server_name". The JID is the identifier on the XMPP network.
Contact list
To save a JID as a contact, you can add them to your contact list (also known as a roster).
Presence subscription
To see a contact's online status (Available, Free for Chat, Busy, Do not Disturb, Not Available) and their current OMEMO keys, you will need to send a presence subscription request. The contact will have to approve your request, and then broadcast their presence data to you. After approval they will also usually request to see your online status too, which you would approve in return.
To streamline the process, most clients send a presence subscription request right when you add a contact, and pre-emptively accept their subscription request in return. So in modern XMPP, to "add a contact" usually means to go through this process as a whole.
However, it is still possible to add someone without asking for presence, or to see a contact's presence without sending yours. This kind of flexibility and respect for confidentiality is generally unknown to other messaging systems, particularly those that use the phone number as the id and rummage through the phone book assigning to anyone they find the contact status.