Originally Posted by MHG

THALYS is in fact an international "TGV".
So, Thalys is a brand but also runs as a separate company (shareholders are the respective railway companies of the countries the trains pass through. (that being the Netherlands/France/Germany/Belgium )
Some TGVīs are also "international" by going from Paris to Geneva in Switzerland. Also Lille-Brussels is a TGV line (or at least it was until recently)
From june there will be a TGV line running form Paris to either Frankfurt or Stuttgart/Munich)
The german "ICE" is just a brand although some units are owned by the dutch railway company.
It also goes international from Germany (to Vienna/Zurich/Amsterdam/Brussels)
In Spain thereīs the AVE which runs only domestic.(donīt know much about it)