Tried 3 different times at 2 different stations with same result. Nozzle says full, guage says half.
tl;dr: it sounds like your fuel tank vent hose is blocked. Find the obstruction and fuel should go in fine.
Here's a quick diagnosis technique: try putting in more fuel while pressing the little white button under the gas cap (it's white on my car). That releases vapor pressure right in front of you. If fuel goes in better while pressing that button, the vent hose is almost certainly blocked.
I had a similar problem with a straight-forward but gross solution. In my case, the vent hose was blocked, causing the pump to read a build-up of vapor pressure as a full tank.
Remember that the fuel tank isn't just a bottomless pit: when you put fuel in there, the liquid needs to displace the air and fuel vapors. That is why there is a vent hose (usually running through a charcoal canister or similar in order to catch the waste vapors).
In my case, we have one car that spends a lot of time outdoors while my older son is at college. A whole civilization of mice has built a multi-story complex of nests in the rear bumper and fuel tank area. Eventually, this almost completely blocked the vent hose, making it nearly impossible to get more fuel in before the pump clicked off.
Solution: clean the accursed mice nests out of the area. Result: fuel goes in!
Have you checked the tank? Has someone fitted the wrong cap to the tank? Or is the tank breather blocked?
I ask because there was a model of car that had a mechanical pump which could suck the tank "flat" : it would only hold 3 gallons instead of the 12 it should do! And the solution was to replace the tank and the "wrong" cap...