Heater hose restrictor and splicers
The 5/8" heater hose splicer on the left functions as a heater hose restrictor, which is often necessary to insure proper cooling by forcing more coolant through the radiator, instead of going through the heater core.
Most cars come from the factory with some type of restrictor. Sometimes, the heater valve acts as the restrictor. Sometimes the heater hose fittingon the engine block is the restrictor. Some cars, like 1992-1996 Corvettes and Camaros, have a restrictor in the heater hose that functions similarly to the part shown above.
The restricted heater hose fitting also protects heater cores when the engine is run at high speeds and the water pump creates high pressures that can damage heater cores.
Normally, if a car has 5/8" and 3/4" heater hoses, the small hose is for coolant going into the heater core, and the larger heater hose returns coolant.
The fitting on the right is a transitional 5/8" to 3/4" heater hose splicer. This is useful on engine swaps such as an LS1 into a Mazda RX-7 because the water pump on the LS1 uses a 3/4" fitting, and Mazda RX-7 uses 5/8" heater hoses.