New Yorker Boiler Coexisting with Hot Water Heater

I appreciate this forum and the patience with my lack of knowledge and these very basic queries. I have a New Yorker Boiler and a separate hot water heater. The boiler was installed long before the water heater. I want to question how the boiler impacts domestic hot water. I observe the pipes running from the boiler to the hot water heater. I have domestic hot water whether the boiler is running (on) or not (off for periods of time such as summer), however domestic water is noticeably hotter when the boiler is on. I assume the boiler feeds hot water to the water heater and ALL domestic water is sourced from the water heater tank? The boiler limit settings (140/180) are higher than the water heater setting (125) which tells me the hot(ter) water from the boiler is producing domestic hot water but I assume it's not direct to the faucets but through the hot water tank? When the boiler is off the (unheated) water still flows from the boiler to the hot water tank? A primer of a few sentences or link to a website that may offer a layman explanation of such a system would be very much appreciated, although I realize many different systems and configurations exist and one may not be able to address my questions without knowing my exact system configuration. I'd be happy to post photos or videos but I do not wish to be even more annoying! Thanks again!