Different Camshafts, Different gaps, Why?

One small reason is that quiet running is sometimes a consideration for marketing road bikes.

The hotter/wilder the camshaft, the more likely the lobe profiles are going to be very extreme. With massive valve lift and strange opening/closing times. The non-normal tappet gaps used with these sporty camshafts are to help delay the opening/closing times which in turn then allows each valve to operate in its optimum design power range. The breathing of the engine being a significant factor here. 
More simply...... the bigger tappet gaps stops the follower touching the camshaft lobes too early and in turn opening or closing valves too soon..

It's to do with the design of the opening/closing ramps on the cam. For racing I use an extreme cam, but it's designed for .006/.008 gaps .. it lifts a lot more than 4s etc

Just as there are different gap settings for tappet clearances depending upon the camshaft, cams themselves can perform in different ways.  I have a 4S camshaft, because it was the only one which was readily available when my engine was last assembled.  I didn't want to run the specified 12 and 16 settings because I had heard an engine running with those settings and you could hear the tappets coming around the corner before the bike came into view.  I asked Pete Lovell for advice and he said to stick to 6 and 8, which I did for many years.  I now use different settings following advice from someone who worked on the Domiracer project but I am also using just the large valve springs because I don't use the upper range for revs - 5-7,000rpm.  My engine seems extremely tractable with the single 32mm Amal concentric carburettor [and no air filter] but there's plenty of 'Go' when I need it, despite the changes to valve springs and clearances.  Acceleration could be slightly crisper but the whole plot is much smoother.  As ever, your mileage, and experiences with cams and clearances may differ.  If you want the definitive explanation for cams, quietening ramps and clearances etc. then contact Philip at Triple Cycles. 

Somewhere I read (I think by Peter Williams) that the gaps on his Commando were .012" because the quietening ramps were .012".  That makes no sense to me...why have quietening ramps if they aren't touched by the valve gear?
Should we check when hot?  Were the wider clearances on 650SS due to the camshaft changes, or the then-new alloy pushrods?

I think the noise/shock  reducing  ramps make unwanted changes to the openning and closing timing that the cam designer aimed  for and the clearance compensates and  allows the cam to perform closely  to its design parameters. When i set the timing on my bevel drive OHC i adjust the clearances to get the relationship ex closing /inlet opening  close to the  design settings by playing with the clearances but still allowing enough for heat expansion . Seems to work. Revs off the clock. Have to back off to avoid a big bang.

I was watching a video by Jim Schmidt the other day that (if I remember right) said that with steeper ramps the tappet could accelerate so fast it lifts off from the cam lobe at high revs. Could this be a factor?

Dave and John are bang on, the cam design and the ramp dictates the clearances, I think PW was describing it in simple way, when you look at grind data you can see why.  Expansion due to heat will affect the clearance, but the difference is very very small compared to the clearance gap when set correctly and is nearly insignificant. Larger cam lift will also have an effect on the design of the base circle, clearance circle etc so that acceleration of lift can be within sensible parameters. However, like most things there is a trade off, if for instance you had a standard cam and just made the lobe larger for more lift the follower would be in contact with the cam longer, the cam rotates at the same speed, but the distance travelled by the follower on the cam is longer but covered in the same time frame, thus more heat and more wear at the interface. Thus begins the 'if we change A, we can achieve B, but then end with issue C' getting the balance correct by trading one off against the other is the fine art. 
Cam design for the Norton twin, the main issue is that the working envelope is restricted and thus only so much can be done with the space available and within the parameters of cam design to have a working cam. 
Just before PW passed away he sent me a link to a very good cam design publication, in his words, it explains cam design in relatively easy terms. Though it does need reading a few times to grasp the detail. I may still have the link if anyone wants it. 

I have a dial guage and am hoping to borrow another so i can map out the cam timing on a graph and see if it accurately follows what the designer intended. I suspect that due to the worn machinery that Norton were using back in the 60's the timing is not always ideal. Some alterations may be needed. I have noticed that some seemingly identical bikes can have very different levels of performance . back in the day we would just shrug and say it was a Friday bike . We used to set up a drag competiton  between our bikes . A late DD head 88SS. a very  chromey highly modified 99SS,  a 650 SS  and my single carb 88 std .   The std 88 was always alongside the other bikes up to about 90 mph  ,usually in front of the 88SS .  I was  asked to swap bikes as the 650's owner was really curious . I  beat him by a good margin  !. perhaps i was just more prepared to rev the bikes out. The 88 was a better bike than the others for 75/80 mph crusing as it was smooth and relaxed. perhaps it had theoreticlly  correct  valve timing ? The motor was never the same after seizing at 90 mph on the M1   on a run from Cumberland to London racing a 3 litre car. 

Could some of you learned gentlemen explain to me why my M50 has zero clearance on the tapets? I have longer push rods than a Domi and cannot believe they expand/ contract any less.
Is it just because my cams are so soft compared to other bikes, but my AJS single is the same, i.e. zero clearance! But My Venom is not (6&8thou)  why should this be? 
Regards John O

It's all to do with expansion . my 500 Rudge was zero clearance too . Iron barrel ,and iron pushrods . Perhaps should be the same on your bike???

If you want my advice, where zero clearance is recommended, give it 0.002" clearance.  It's safer.

... with the Norton handbook figures thanks. Zero clearance has worked for my 19S (iron barrel, alloy rods) for the last 48 years. 

Sounds like you didn't want my advice!

Completely agree with you Ian. I have ridden Norton's since I bought my first 99SS in 1970 and have always used the factory figures whether it's my Commando, s.v. and ohv singles and o.h.c  bikes. The clearances vary from zero for my 1951 ES2 upto10 and 20 thou for the Cammy. Never had a problem with loss of compression or excessive noise on any machine.