I didn't see anyone post the purpose of a red (1st/single stage) regulator, though some hinted at the workings.
A propane bottle stores propane at a high pressure, too high for normal consumption, and keeps a large amount of the propane in liquid form.
The normal propane appliances use low pressure propane vapor, not liquid.
Regulators reduce the high pressure to low pressure.
But....the catch is this pressure reduction (and volume expansion into low pressure gas form) can cause a substantial cooling effect inside the regulator.
For small volumes, not a problem. For higher volume appliances, multiple appliances used at once, or colder outside temps, this can cause freeze ups of the regulator.
Splitting this process into '2 stages' with a red 'high pressure' regulator, then a final low pressure regulator, can reduce this problem and deliver a higher, often more reliable gas flow.
There are '2 stage regulators' that look like a double regulator, but are one unit. But there is no reason these two stages cannot be separated by a length of tubing/pipe.
Think of it this way. Bottle is storage, red/1st stage/high pressure is used for (high volume or "inside") distribution, and 2nd stage/appliance inbuilt/low pressure is for final consumption.
For houses, it is not permitted to run unregulated lp within the structure (directly from bottle/tank). It MUST be reduced at least to 1st stage. It is common to have a 1st stage regulator at the tank or on the outside of the building, thenn thee line enters and branches throughout the building, then have multiple 2nd stage regulators near the points of consumption.
I don't know if that is the same reasoning for DOT regs or what they are, but it would make sense ;)
The important thing is NOT to mix lines of different stages of regulation, and NEVER NEVER NEVER send un-regulated lp to an appliance that does not have the proper regulator.