The OE sensor is 1/2 inch NPT (National Pipe Thread}, a tapered thread - tighten tighter to stop leaking.
Sensor is installed without too much pipe sealant as the sensor body needs to be grounded to the head for circuit continuity.
If you use an ohmmeter, measure the resistance from the center terminal to engine ground.
When cold, reads high resistance, above 1000 ohms.
As the sensor heats up, typical resistance value would be about 180-200 ohms for an approximate gauge reading of 180°F, the 10 o:clock mark.
Reads like the head is set for a 3/8" NPT.
You might be able to drill out the 3/8 hole for a 1/2 hole, I have never done it, yet. Be careful in tapping, you could make the threaded hole too big.
Yes, there is a difference in the sensors you have.
No, you should not 'adapt' to fit the sensor as the sensor tip needs to be in the coolant flow for a correct reading. If the sensor is out from the coolant flow, the gauge will not sense the coolant temp. It may sense cylinder head material temp, and would be a higher temp indicated.