They are different, its complicated, you have mfg tolerance in this.
And a whole new built is just a whole new variable.
So, lets lay it out and figure out, what is the goal here?
Head space is a very poorly understood subject and then opinions get thrown in and it gets mucked up, so good idea to take a deep breath as it really is more than one thing affecting things here.
As noted, to adjust for a lot of variance, the Brits elected to have difference bolt heads.
So, say you have a Number 3, measure all that with head space gauges then do it with a number 1. Changes everything because you have changed one end of your baseline.
Throw in Brit SMLE chambers were "generous " and you can have cases go on round one or (if you reload) no more than 3 (generous in diameter not the length though that too)
Then you have a rimmed case and throw in the variables there (thickness as you note)
So yes for the one ammo type, the head space is too short with the bolt head you have but the other works. Go with that one?
Change it all and you may wind up with ammo that won't fire, because the head space is now so great the case move forward (have to ponder that one, maybe e not with rimmed) - very likely will stretch the cartridge and possibly to rupture.
No, don't invest in a lot of gauges, or bolt heads. Figure out is it ok with the ammo that works?