Vented heaters have a heat exchanger. So they use a flame to heat up air, that air is run across the exchanger to warm it up. That combustion air has tons of water vapor and other combustion gases in it (carbon dioxide and carbon monoxide, etc) and is run up a chimney. Typically, 80% of the fire's heat stays in the space, 20% goes up the chimney (this is referred to as a 80% efficient heater). Others, like my house furnace, can be up to 95% efficient or even a bit higher but at a greater cost and higher mainentance.
Now, that heat exchanger has air tubes in it. Air from the heated space is pulled through and blown back out into the space, heating it in the process and never mixing it with the combustion gases.
A non vented just lights an open flame and spews all that heat and combustion gas into the space. With it comes carbon monoxide, water vapor and all the rest.
