According to the website Space, the distance is 37.8 trillion km.

This is not correct, and is probably the result of rounding the light year distance to 4 ly before converting to km. The google answer is pretty close.

The correct answer is the distance to Alpha Centauri is 41.5 petameters (trillion km) and the distance to Proxima Centauri is 40.2 petameters.