Is Jabber the same thing as XMPP

Also I expect my messages to be delivered in the end independently of whether the peer is online now or not (i.e. eventually the message will arrive when we both will be online).

XMPP servers/clients usually support sending messages to offline contacts. These XEPs might be relevant (maybe there are more):

• XEP-0013: Flexible Offline Message Retrieval
• XEP-0203: Delayed Delivery

I've got used to edit about 30% of my messages in Skype.

I don't know how Skype implemented this, but there is a XEP for editing the last message sent.

XEP-0308: Last Message Correction:

When sending a message, people often introduce typing errors and send a follow-up message to correct them. This specification allows the sending client to flag the second message as correcting the first.

I think OneTeam has implemented this feature (but I'm not sure, never used this client). There may be other clients, too.

/edit: as Zash noted, Swift supports it, too.

Priority and Resource are relevant when you are online with multiple clients (with the same JID).

Let’s say your JID is alice@example.net and you are online with two clients:

• Client 1
  Priority: 5
  Resource: home

• Client 2
  Priority: 7
  Resource: mobile

If someone sends a message to alice@example.net/home,
you will receive it on Client 1.

If someone sends a message to alice@example.net/mobile,
you will receive it on Client 2.

If someone sends a message to alice@example.net,
you will receive it on Client 2, because it has the higher priority.

tl;dr: The Resource allows the sender to identify/target specific clients, and the Priority decides which client will be used in case the sender doesn’t target a specific Resource.

The Priority can go from -128 to 127. If you set a negative Priority (e.g., -1), this client will never receive a message unless the sender explicitly sends it to that’s client Resource. If the clients have the same positive Priority, all of them should get the message.

Some clients append random strings to the Resource (probably what ChatSecure does) to make the full JID unpredictable, which can be relevant for security reasons.