Part of the "confusion" arises from not understanding how a carb actually works. As Rob points out, Piaggio has, on occasion, speced the same jets for a 125 and 150, and the reason is that the two use the same air/fuel ratio and the airflow from the configuration of the two engines is the same.
Rather than retype the basics behind "mixture" I would suggest you read this:
Lean vs Rich - Warning! Technical
Note that mixture is by weight. Of course, your carb does not weigh the air and fuel, but uses volume as a proxy.
The carb incorporates a narrowing in the air flow called a venturi. The air supply increases speed through the venturi, and that causes a drop in pressure. That drop in pressure sucks the fuel out of the atomizer. The faster the air flows through the venturi, the greater the drop in pressure and thus more fuel is sucked from the atomizer,
within the flow limits of the jet. And that flow limit of the jet is set to deliver fuel at approximately a 13.5:1 mixture.
The speed of the air at a given RPM through the carb of a 2T is a result of of a variety of factors, beginning at the entry into carb box and ending at the exhaust. Change any of these factors and you change the speed of the air flow. If that change in speed exceeds the design flow limits of a given jetting configuration, then you will change the mixture. In order to get the correct mixture, the jet configuration must be changed. So, for example, if you replace a stock cat pipe with a SIP Road, you increase air flow and speed, and a larger main jet is required to provide a fuel flow rate that keeps the mixture at the "sweet spot" of about 13.5:1.
Now move on to emissions, as this is what has given rise to the whole thing. Emission standards are expressed in weight of pollutant per mile driven. Thus the objective is to reduce the amount of unburnt fuel per mile. As stated in "
Lean vs Rich" above, a "leaner" mixture burns the fuel more completely ("cleaner") and produces more power, but also has a higher combustion temp. Thus, there are limits to how "lean" a mixture you can incorporate in the engine design to use mixture to reduce pollution, as a too high combustion temp will damage the engine. If a cleaner burning mixture is insufficient to meet emissions standards, then the next step is to reduce the air/fuel consumption per mile, while still retaining the magic 13.5:1. This can be done by restricting aspiration on the intake and/or exhaust side. And, a cat exhaust can both restrict aspiration and perform some cleaning of the exhaust gases.
Also, since there is a limit on how much air, and at what velocity, a given diameter venturi can move the intake mix, the use of a smaller diameter carb can also reduce emissions, which was the case with the US market P200s. Straying a bit off topic, this is the reason for 2 and 4 barrel carbs, with smaller venturis working to each deliver a portion of the air/fuel mix at a velocity and volume that is greater than a single barrel can effectively deliver, but far less than 2X a single barrel.
So, when we change the aspiration by drilling out the air filter or replacing the cat exhaust, for example, we change the speed of the airflow through the venturi. If the installed jets' design flow rate cannot deliver the necessary volume of fuel to maintain 13.5:1, they need to be changed. "Upjetting" is not making the mixture "richer", but keeping the mixture constant, or at least within correct limits.
So, within limits, it is possible to configure a 125 and 150 to consume the same amount of air/fuel mixture per mile, and thus use the same jetting configuration. Obviously, there will be performance impacts, but if the objective is emissions control, in a very simple engine like ours, that is unavoidable.
Lastly, as seen on the Euro 3 Vespas, variable timing can also provide cleaner burning over the RPM range, and a rev limiter can keep the engine from RPM where emissions exceed the limit. But these features do no affect aspiration, the primary topic being addressed.
Make sense?