I’m no expert but here goes...
The cartridge case dimensions are the same between all 3.
The difference in the chambers is primarily in the leade area. 5.56 has a longer leade and different throat angle (why it’s said higher pressure 5.56 ammunition shouldn’t be fired in a .223Rem chamber). .223 Wylde is somewhat of a hybrid of the 2, it has a throat length and angle similar to a 5.56 chamber with the smaller freebore diameter of .223Rem (.224), meant to be accurate with .223Rem ammunition while remaining safe to fire 5.56. This is all going to also depend on the particular reamer being used to manufacture the barrel.
The headspace dimension to the datum line of .330 is the same between all of them though.
SAAMI specs for the .223Rem are minimum headspace of 1.4636 and maximum of 1.4736. There are no SAAMI specs for 5.56 NATO.
That being said here is the chart of the headspace gauge sizes straight from Forster, one manufacturer of headspace gauges.
Personally I use the .223Rem go and no go gauges from Clymer but they are the same dimension as the Forster.
What some guys are using as a “5.56 no-go” is actually the 5.56 max gauge, which is 1.4736 and could still have I would consider excessive headspace for sure especially on a new build, and I would be changing parts if something I assembled was larger than a .223Rem Field gauge (1.4696). This also means that failing a .223Rem no-go (bolt closing on 1.4666) does not mean that your gun is unsafe to shoot, but does mean that you should be doing some more checking and/or swapping bolts if ultimate accuracy is your goal.
Something worth mentioning as well is that headspace checks should be done with the extractor and ejector removed from your bolt, and are easier to do before the barrel is installed in the upper if this is a new build.
Apologizes for the long-winded post but there seems to be a lot of confusion on this forum in regards to headspace especially with all the assembling of these great new NR options on the market.