Between Amsterdam and Paris you are within the Schengen zone.
UK to Europe will have border control, passports, etc.
UK to Europe will have border control, passports, etc.
But re: UK<->mainland I guess it shouldn't be surprising that there's more security for the Chunnel crossing. That feels like it would be a much more likely terrorist target than a random HSR route on land.
A few years back Thalys merged with Eurostar and then last year they started rebranding the former Thalys services as Eurostar, too, which probably explains the confusion.
Only the former Eurostar services (nowadays "Eurostar Blue") have the security theatre on account of the Channel Tunnel plus UK being non-Schengen, whereas the former Thalys services ("Eurostar Red") are regular train services just like in the rest of Europe (except for Spain, which does some security theatre for its high speed trains, too, although AFAIK a bit less intense than Eurostar, which in turn is less intense than flying).