Stupid Question Department; What does the relay do that the aquastat doesn’t do?
I'm not an electrician, so this comment is just based on my practical knowledge, whether or not I know what I am talking about. Also, my comments are unrelated to any code requirements, and following the code is important.
An aquastat opens/closes contacts for a circuit based on a temperature setting. If the intent is to control a circ, this can be done directly from an aquastat, but since the circ requires line voltage, the aquastat must have the hot wire from the line controlled by the aquastat contacts.
Or, have a low voltage control circuit (24VAC) controlled by an aquastat/thermostat, wired in series with a 24VAC relay coil, and a transformer providing 24VAC power. The aquastat/thermostat device opens/closes 24VAC power to the relay coil, which opens/closes the relay contacts. The line voltage is wired to the relay contacts to control the circ. It generally is less expensive and less line loss to use a 24VAC control circuit, and then keep the line voltage wiring limited to what it actually has to power. Possibly also some safety issues running line voltage control/load circuits, but if done properly, I'm not aware that there is a safety concern.
Depending on what is being controlled, it is possible that the contact ratings of an aquastat would not be rated for the load being controlled. In this case a relay/contactor would have to be used, with the aquastat controlling the coil, and the load served through the relay/contactor contacts rated for the load being controlled.
My system is compact and I use line voltage aquastats to control the circs. I also have a 12000W backup tankless water heater as freeze protection. The tankless water heater has a 24VAC control circuit with a contactor relay to control the 240V line feed to the heater.