No, the oldschool is agent for those things for which it was agent.

An agent may or may not also be a daemon. It can be a cron job where the only daemon was cron not the agent, and the agent doesn't persist and isn't a daemon.

It can be purely ephemeral where the only daemon was ssh or http or any other other generic communication service that is merely how the agent was delivered.

Countless ordinary "things that run on a host and perform tasks for some other host" were always called agents. Some of those were also daemons, just as they were also programs.

Nagios, crowdstrike, chef, puppet, ansible, vmware/kvm/virtualbox, jenkins... etc all have a slave part that runs (usually in the form of a daemon) which is and always was called the agent.