Assistant. An assistant typically responds to a user request, helps reason about information and may prepare work for the user to approve.
Agent.
An agent can pursue a goal across multiple steps, use tools, inspect results and decide what to do next within defined permissions.
The important difference is not chat versus no chat. It is how much autonomy the system has, which tools it can use and what actions it can take.
The autonomy tradeoff.
More autonomy increases leverage but also raises the need for permissions, observability, fallbacks and evaluation.
How to choose.
Use assistants for interactive knowledge work and agents where repeated multi-step actions justify the operational complexity.