The barbecue regulator goes from tank to barbecue pressure. The residential propane tank regulator goes from tank pressure to 11" line pressure.
The assumption that every device in the home has its own diaphragm regulator from line pressure to manifold is not so simple or clear.
Depending on the needed flow that diaphragm regulator can be the size of a dime or the size of a silver dollar... They all have something built in or on.
The large unit outside the home steps down from line pressure using a diaphragm to get an output pressure that is standard for residential and compensate for relative pressure around the house... i.e. I live at 9000ft and my pressure is only around 11.2 PSI where at sea level the pressure is 14.7 psi. They would also compensate for pressure changes due to the weather - i.e. a shift from 28inhg to 31inhg ... standard sea level pressure is 29.92inhg...
There is a lot going on in the outside units on a house including the meter than counts how much gas you use.
Interesting fact - the gas company once scheduled with me to swap out the meter - they are required by the PUC to send in X number of meters every year to be calibrated and check that they are counting correctly.
My furnace is 90,000 btu, the dryer is 22,000btu, the water heater is 60,000btu, the stove is 9k btu per burner and 18k for the oven part. A gas grill can be between 10k and 40k depending on the grill...
Vast difference is amount of gas to burn to heat the various appliances burn so a large difference in diaphragms and regulators....
My furnace has a 3/4" pipe... the water heater is also a 3/4" pipe... the stove is 1/2" and the dryer is 1/2"... this affects how much gas can flow... when I recently had to replace a leaking flex line I used 5/8" for the furnace that was rated at 120k btus.
And the diaphragm size for a grill is almost always propane and is sized depending on how many items are connected. My old grill had a burner on the side plus 4 of the burners in the grill area. There were 2 lines from the grill and two regulators - one to the burner and one to the grill area.
I am pellet smoker now.