Not exactly.
A condensing heating device is simply one that extracts enough heat to lower the exhaust flue temperature into the water condensing range. Different sources make different claims, typically from ~250F and lower, some can approach an exhaust temperature slightly lower than the discharge temperature of the heated media.
And for some fun check the recommended temperature to prevent Legionella and the max safe hot water discharge temperature.
Lower domestic hot water temperatures are more efficient but tend to promote Legionella.
They use a collection tank and lift pump into the sanitary sewer.