What is the difference between full & conversation recording and their use-cases.

The full recording captures all aspects of the call, including pre-call (such as the hold music ) and also the actual conversation between the agent and customer.
Conversation recording, on the other hand, captures only the conversation between the agent and the customer, excluding any hold times or transfers.

This configuration is available on the Skills configuration page.

Double-click on any skill to edit the skill and change the Record option to Full or Convention and click on the 'save' button as shown below.