Agent is a light weight program running on the target computers where we want the automated process to run. Eg: Windows/Unix agent. Agents execute server commands on Tidal's behalf.
Adapter is a software that translates information between Tidal master server and target server or agent. Eg: Informatica Adapter
In Tidal, not all adapters require an agent to be installed on the target server. Eg: Informatica, MSSQL
The reason is that, Cisco have worked with other product vendors such as Informatica and Microsoft in the above example, so that the adapter is able to natively communicate with their products. So indirectly, the Informatica and MSSQL services running on the target systems act as the agent, which runs the command on Tidal's behalf
You will also notice agent-less adapters in Tidal.
Hope this helps
These are not textbook definitions. They are certainly available on google :)