Older boiler with embedded hot water coils are typically operated high & low limit aquastat controlling the burner, as well as a high-temp safety limit.
The room thermostat often only controls the system pumps, and when water is flowing through the boiler, and the burner doesn't fire until it is cooled by the water flow down to the low-limit aquastat setting, after which the burner fires until it's temp reaches the high-limit. Similarly, when potable water is flowing through the coil the boiler doesn't fire until that flow cools the water to the low-limit setting. Once the low-limit aquastat kicks on the burner, it always fires until the high-limit aquastat is satisfied, whether the potable or heating water is still flowing or not.
There are "smart" economizers (eg, Intellicon 3250, or Beckett Heat Manager ) that can be retrofitted to optimize the operation, which anticipate the end of a call for heat from the thermostat or HW draws base on prior system behavior (they "learn" the system), kicking off the burner at some lower temperature, constantly adjusting the actual high-limit. By parking the boiler at a lower temp at the end of a call for heat than it otherwise would they save quite a bit standby losses (a hotter boiler loses heat faster than a cooler boiler.) Many newer-smarter boilers have these sorts of controls built-in, but most older boilers can be retrofitted, and double-digit percentage fuel savings over a season are common.
With embedded coil hot water heating the low-limit is usually set fairly high to handle the cooler wintertime incoming water, but it can be tweaked down for the warmer seasons, for a substantial savings as well. With an oil fired boiler you can't drop below 140F without some risk of damaging flue condensation, but with gas or propane that can be safely dropped to 130F, if it's still meeting your hot water needs.
Heating hot water with an "indirect" tank operated as a separate zone can usually let the boiler cool between calls for heat/HW for even lower standby losses, but the controls are slightly more complex. Some oil-boilers can't be cold-started frequently with out sustaining undue wear-& tear, but most gas boilers can. In cold-start mode the boiler needs to be brought up to the min-temp before allowing the circulation pumps to distribute the heat, so the burner is controlled more directly by the room thermostat (or the indirect-tank's aquastat), but as a system it's usually more efficient, and usually delivers higher hot-water flow rates, etc.