Furnaces are sorted into venting categories by how hot and how pressurized their exhaust is. A standard 80% AFUE furnace is Category I: its exhaust leaves at roughly 300 to 500°F and rises by natural draft up a metal Type B vent or a masonry chimney. A high-efficiency 90%+ condensing furnace is Category IV: it has cooled the exhaust below about 140°F to wring out the heat, so the flue gas is cool, damp, and slightly acidic, and it is pushed out through PVC or CPVC plastic pipe, usually through a sidewall, along with a condensate drain.
That difference is why an 80%-to-95% replacement is not just a box swap. You cannot run a condensing furnace's acidic exhaust up the old metal vent — it corrodes the pipe and can leak carbon monoxide — so the job includes new plastic venting and a drain. A reputable contractor prices that in; a suspiciously cheap condensing-furnace quote that says nothing about re-venting is a flag.
The detail almost everyone misses is the orphaned water heater. In many homes an 80% furnace shared a chimney with the gas water heater, and the chimney was sized for both. Pull the furnace out for a sidewall-vented condensing unit and the water heater is left alone on a flue that is now far too big for it. Its exhaust no longer has enough heat to climb the oversized chimney, so it can spill — backdraft — combustion gases, including carbon monoxide, into the house. The fix is routine when it is planned for: a correctly resized Type B chimney liner (or a power-vented water heater). The danger is when it is ignored. Ask any contractor quoting a condensing furnace how they will handle the water heater's venting.