DIDComm peer-to-peer messages are asynchronous messages that one agent sends to another - for example, Faber would send to Alice. In between, there may be other agents and message processing, but at the edges, Faber appears to be messaging directly with Alice using encryption based on the DIDs and DIDDocs that the two shared when establishing a connection. The messages are JSON-LD-friendly messages with a "type" that defines the namespace, protocol, protocol version and type of the message, an "id" that is GUID for the message, and additional fields as required by the message type.
Link: Message Types
As protocols are executed, the data associated with the protocol is stored in the (currently named) wallet of the agent. The data primarily consists of the state object for that instance of the protocol, and any artifacts of running the protocol. For example, when establishing a connection, the metadata associated with the connection (DIDs, DID Documents and private keys) is stored in the agent's wallet. Likewise, ledger data is cached in the wallet (DIDs, schema, credential definitions, etc.) and credentials. This is taken care of by the Aries agent and the protocols configured into the agent.
In addition to protocol specific data elements in messages, messages can include "decorators", standardized message elements that define cross-cutting behavior. The most common example is the "thread" decorator, which is used to link the messages in a protocol instance. As messages go back and forth between agents to complete an instance of a protocol (e.g. issuing a credential), the thread decorator data elements let the agents know to which protocol instance the message belongs. Other currently defined examples of decorators include attachments, localization, tracing and timing. Decorators are often processed by the core of the agent, but some are processed by the protocol message handlers. For example, the thread decorator processed to retrieve the protocol state object for that instance (thread) of the protocol before control is passed to the protocol message handler.