Curious if anyone else has put any thought in comparing companies like Square and Stripe to the early goals of American Express (AMEX)?

Opinion (don't read on if you are looking for hard facts):

The way I look at it, AMEX designed a closed loop payment system to easily ensure payments between customers and merchants.

Square and Stripe seem to be trying to accomplish the same goal, but in the 21st century.

Strictly calling Square a tech company, would be like calling 20th century AMEX a paper processing company--or maybe I am misinterpreting the founder's point.