Modern Vespa

Who makes the Vespa 300 motor/
do they build them or an outside scorce
older guy

Inhouse...

Designed and built by Piaggio, the Italian manufacturer of the Vespa.

Despite what you might read on the internet, Piaggio engines are not made by some guy in England named Steve.
Piaggio manufactures their own engines. They do farm out a lot of the components, which is fairly common.
Historically, Piaggio has a very interesting relationship with Honda, who they have bought engines from in the past. Honda has done a lot for and with Piaggio over the years, and they seem to use a lot of the same suppliers.

... now it's all globalized ...If you don't work by globalizing the components then close, even external suppliers do it (electrical parts, carburetors, wheel rims, tires, etc.). As has been said in other topics, the difference is made by the quality control which "should" be better if the manufacturer checks the finished product again. All follow this procedure.